Who is immortal? Do any of those people who had passed away, visit the world? Immortality has many aspects:
If immortality is to mean "living somewhere, in some sense," then everybody is immortal - as acknowledged by Islam, Christianity, etc. We are informed that, the spirit lives forever. After we are referred-to as "dead," we [may] wait in tomb, until the judgment day. Next, every human, and every genie are sorted with their heavenly vs. hellish status.
Furthermore, there are hadiths of our prophet Muhammed (s.a.s.), inform about the people in their tombs. The "death" (in tomb) is not a blank period. They feel bliss, or pain, there - mainly based on whether they were good, faithful people, or sinners, non-believers.
There are things we may do for the sinners, too. e.g: Plants, planted for them, improve their condition, because a plant is an innocent, living organism, worshipping Allah - even if we do not hear that. It is as if we hire those plants, to work for us, or for the tomb-resident. (Plant it where it does not hurt anybody. e.g: Not on a road where it would obstruct people's passage, but at an edge of a road, or at an edge of the tomb, etc.)
Was Jesus (a.s.) killed? No. Judas was killed, instead. Allah illusioned them. Jesus (a.s.) was saved, and we wait him to return - alive, as he is. In Quran, en-Nisa(4):157 refers to it: Jesus (a.s.) was not killed.
This concept is very fine, with the rest of the Islam. For example, a hadith of our prophet Muhammed (s.a.s.) informs about time in the other-world versus in this-world. A thousand-years of this-world, corresponds to a single day of the other-world (in heaven, or hell). When waiting in heaven, in two thousand years, by earth time, Jesus (a.s.) might have passed only two days of his life. That means, he return at the very age he had went away - only two days older.
This relativity of time, may fit the relativity-of-time in physics, too, as others point out. This page is not about physics, but here is the pointer.
I have heard, but not read yet, about a commentary that suggests (a possibility) that the return of Jesus (a.s.) might be as a phenomenal-presence, rather than bodily return. But I cannot figure out, in such a case, how we would explain the news about what he would do, when he returns. I do wait him to return.
The popular figures, Hizir (a.s.), Ilyas (a.s.), and Santa Claus, are in fantasies of many. Are they alive, at all?
Opinions differ. I tell what I find probable. These are not any original ideas. Many other people think this way, too. i.e: This only lists what I prefer, as the most-probable-case judgment, even if neither original, nor necessarily conclusive.
There is no acknowledgement about Santa Claus, in Islamic sources.
The Hizir (a.s.) case is controversial. The Ilyas (a.s.) case is similar to the Hizir (a.s.) case. Were they prophets? Were they awliyah (saints)? Do they still live? Or, are those two persons, two public-posts, where Allah assigns a new person, each time? (e.g: similar to the concept of the finest-40-people, the 40-awliyah)
I respond: Hizir (a.s.) is probably, a public-post. Some of them might have lived long, too. I do not readily subscribe to the theories guessing he is older than a thousand years, because in Quran, there is a statement that tells we live in this-world for a single day, or less (by the other-worldly time). Allah may do exceptions, but why should I assume that?
Allah, in Quran, points out that, He has let Jesus (a.s.) born as an exceptional case, to a chaste mother, without any touch of any men. Allah asserts that He is able to create, in any way. If about Hizir (a.s.), there were any such acknowledgements, I would accept that as yet another exceptional case (this time, about life-length), but there are no such exception-statements about Hizir (a.s.), in Quran.
As a black humor, I may only warn you that, Hizir (a.s.) is not reported to charge anybody, any money, for any of the help expected from "the Hizir (a.s.)." Therefore, if a door-to-door salesman, or an internet e-mail asks you money, in return for "Hizir-help," simply do not buy it. After I point this out, I expect the potential of an abuse is not there, any more. :-)
There are examples of preserved corpses, since millenia - without any special treatment. This is acknowledged by Islam, too. We are informed that, the soil does not eat the corpses of several types of people. Except a single case, they were/are the firm, rightful people.
Even that single, evil-side exception, is known to do the right thing, at least, at that moment of death, when the sea was closing and death was clear-and-present, after Moses (a.s.) and his people had passed. His death-moment words are reported to be "I believe the God of Moses (a.s.)" - although it is believed to be too late, and not to be accepted, any more. (Quran refers to other such cases, too, any way. People who pray only to the God, when violent waves beat their ships, but leave that appeal, at the shore, and may be involved with any number of evil, too. That was not the first miracle of Moses (a.s.), any way. And even the very people who saw the sea-split, as they were saved, later could go on to commit several cases of opposition, against Moses (a.s.). Quran mentions those cases, too.)
I have not heard any explanation about the measurable/tangible reasons for it - except the personality-profiles told by our prophet Muhammed (s.a.s.). It simply exists, but we do not know whether Allah has built it into the organism. Let's formulate a few research hypotheses for a theory.
Is it a built-in, measurable feature of a firm-person, who were [killed while] doing the right thing? (The fair-rulers, shehid, evliya, prophets, fit that.)
I know that some corpses of animals/plants, etc. may not rot, if their skins would not contain the water to let the bacteria to operate on them. But, is there any such bio-measurable indicator that would sort a firm-rightful person, the gooood vs. the average vs. the extra-lax vs. the evil?
If such a measurable chemistry exists, is it measurable, when these fine people are living, too? Or else, does Allah preserve those corpses, as an extra miracle?
I do not know of any research about it, yet. But from other examples, I infer that Allah documents his acts, and He intervenes within the rules, He had set for the universe. i.e: It is extremely-improbable cases to exist, but when evidences are there, it is very easy to verify.
For example, the very sea-split of Moses (a.s.) were suggested as a possible result of a known volcano-eruption that day, in a remote island. But, how would those shock-waves arrive and realize as a sea-split to twelve paths, exactly at that very moment, when Moses (a.s.) arrived there, prayed and hit his stick at the sea? Whose timing is it? That is Allah, who arranges them.
In Quran (2:154, 3:169), it is written that, the shehid people, those who were killed while fighting for Allah, are not dead. ("Do not refer to them as dead. They are alive, but you cannot see.")
A shehid is already one of those whose flesh is not eaten by the soil. How about the others? Are they alive, too? Do any of the non-dead (although buried, etc.) people visit the living?
In Quran, some people are referred to as alive, although with a phrase that, we cannot see them. Is that "never see," or "not always see?" Informed by the various reports of phenomena, we interpret it that, although they are not always seen, they may visit - possibly by some extra permission of Allah - per specific event, or per specific cause, etc.
Do any tomb-residents respond, from their tombs, if talked to them? There are reports of such, too. e.g: Our prophet, Muhammed (s.a.s.) is reported to have responded to Ahmed-er-Rufai (k.s.). That is a specific cause, too, though, as he was there to verify (as a public statement) that he is really a descendent of him. The visits and responses do not appear to be about any tea-party, or such. Therefore, to expect a visit, or a response, is not necessarily so different.
Allah, the God, may let some people to visit us, after we bury their flesh, too. This is quite unlike the deadroids, though. The reported phenomena are different, too. The first point is that, unlike (most of the) deadroids, they appear with their own human-appearance. They do not communicate through (magnoon) mediums, or such.
In any case, though, this also lets itself to abuse, especially where the abuser knew the dead-person, and/or learned about him/her through the genies. Next, one of the abusers, may wear a make-up, and/or with illusion-trickery (e.g: holography), may make you believe that he/she is that dead person.
Although such a case is not known to me, the widespread availability of deadroids which bring secrets of dead-people, coupled with trickery through plastic-surgery which prepare the impostors to imitate others, do suggest that, some charlatans may attempt to trick people about the dead people, too.
Such charlatans may be claiming themselves as the dead-person, to collect money, or to suggest something, in the name of the dead.
Islam (law) orders that, when he/she is "dead" (buried, drowned, etc.), his/her properties pass to the inheritors, and his/her marriage is [temporarily] over. The real visitors would not ask, by any theory, anything for themselves, any way. They do not need anything, there.
The marriages are probably forever. The requirement for a reunion is that, both of them must go to heaven, and the wife must not marry, in this world, after his death. As far as this-worldly case is concerned, though, the marriage is over upon death - until that reunion in heaven.
Keep these in mind. Ready remedy for muslims.
The most important piece is already said, but we may fine-tune our strategies even further, with a few rules-of-thumb. What may a real, or impostor visitor, tell about? How may we respond?
Avoid surprises. For example, when alive, I never ask money from you. I do not ask you to donate anywhere, either. I do not suggest you to join any club, or to marry any specific person, either. I would not suggest you anything, other than what (sunni) Islam allows/suggests. If somebody, on my behalf, even in my appearance, suggests anything, and very especially, if this takes place "in private," then you should only be alarmed. Similarly, your boss could also tell you what never-to-do, even if somebody looks like him/her.
Just as somebody could wear the face of your boss (through make-up, or plastic-surgery, etc.), he/she may do it after a dead person, too. (This may be also about a person who is, in fact dead, or in seclusion, but the impostor circles in public.) Keep alert, to avoid abuses, when holding responsibilities, and/or when your (critical) resources are in question.
Keep the same criteria, when evaluating the offers, either from a dead, or a living person. (Except that we may possibly never reach out to the dead, to verify that it is really him/her who visits, or whether he is somewhere else (through telephone, etc.) This is possibly not so easy, always, for those who are assumed-living, either. But, it is more probable, presumably.) ((Telephone-interlopping, sound-imitation, even privacy-breachers, out there, too. But if those were authenticated/blocked already, we may verify through telephone, etc., too.))
A "full treatment" of this rule-of-thumb may be termed "paranoia" if not further - a publicly-organized-paranoia against impostors. But at those points where easy points/protocols help you identify where it is meaningful to reject some offer, it is possibly very preferrable, too.
Islam does not acknowledge any reincarnation phenomena. We do not find any reason to believe it, by our own experiences, either. The reported phenomena, even the birth-marks, may be produced through electromagnetism. Therefore, they are very readily explainable away, as the (old-time) genies, or the (last century invention) machinery, to transfer those effects to another organism - maybe while a genie leaves the person it stucked with, to the newer target. It would carry the memories, along with it, any way.
The so-called "recalled reincarnation" cases are reported to be limited within 1500 years, which is the lifetime of a genie.
There is a very wide overlap of the phenomena which had been attributed to the genies since millenia, and what are achievable through even patented technologies, since the 20th century. I have discussed some of them, which may be used to commit soul attacks, as a tool of the trouble-maker witch-beings. Those technologies may be used to invoke "deja vue," too - exactly as genies also could, without any machinery, but with their natural contagiousness. This is the trivial part.
The cellular-disease transfer through internal-electromagnetics/electrodynamics is known since 1960s - even if it is possibly still not known, how or why, it works. This does suggest the explanation for those birtmarks, too.
Next, about the ideology of "reincarnation," as a muslim, I may point at the satan, and other deadroids (the lieful genies), which may tell people about such. They suggest other such varieties of "eternal cosmos" faiths, too, any way. The so-called reincarnation may be only one of them.
The anti-abuse strategies page warns about a variety of tricks and traps.