I don't think anyone has the sufficient information to answer that question. It is impossible to say what will happen using simple logic. Logic is based on experience and this question is actually trying to find an answer to a never-experienced situation. The only answer can be null (there is no answer) until someone experiences it.

?1 = Nothing would happen to his past self, his past self has no knowledge of his future self and thus is unaffected.
?2 = If his 22 year old self chooses to meet his 18 year old self or his 18 year old self happens to meet a person he looks like, except older. Clearly the 22 year old self has the upper hand in such an encounter.
?3 = No not on a time "line". However, if time were spherical and not liner, possibly.

Perhaps this situation has occured. Since we are not the person from the future we would have no knowledge of the encounter being anything more then seeing someone who looks similar to ourself. The answer is null for 18 year old John (us today), not for 22 year old John (us in the future).

A more interesting question is if 22 year old John kills 18 year old John (Assuming they could co-exist, and that both would be unaffected as such), would 22 year old John cease to exist? If so, would he just disappear into thin air the moment 22 year old Johns physical form affected 18 year old Johns physical form? But then how could you explain the matter that composed 22 year old Johns physical form just disappearing? Was it destroyed? Would that create dark matter in its place? And if 22 year old Johns existance ceased because of 18 year old Johns death, that would mean that 22 year old John's existance was still linked to the future, and thus the past back to 18 year old Johns existance by a proverbial string. Therefore if they are connected by the same lifeline, they are not seperate entities and could not co-exist, thereby nullifying this whole situation. Any one answer creates 20 more questions. So discussion is moot. Craziness

No one knows...

They actually do co-exist in one so-called time-line.
The 18 years old John exist in the 22 years old John's time-line.It is his part,even been only as a memory that covers the larger part of his memory in been.
So in one direction, the "forward" one, they are the one John's self.
Hypothetically if there is a way to travel 4 years back in "time" for John(the 22 years old)he has to be the same one John's self (the 18 years old)at that point in time.The question boils down to;"can the number 22 fit in the number 18 ?!"
Hypothetically if considering the self as able to expand and allow for a such a fit in - then the 18 years old John and the 22 years old John will be the one and the same John with a memory expanding four years in the future from that point in time.

This is only a hypothetical view or angle to look at the subject you forwarded in this discussion.

cheers

(hypothetically)
Time is not one line but an everbranching tree.
Every second the entire universe splits up into an infinite amount of slightly different possibillities.
So there are an infinite to the power of an infite universae.
You can go back in only one line and meet and even kill yourself, but you won't ever be able to return to your previous future. The future you will end up in is unpredictable because the variables (positions of all the atoms and stuff) have been changed by you being in that past.
That time branches is logical. Many things in the universe branch. Trees, our brain, arteries, species of life, rivers, lightning, solar flairs. And it also forms a closed circuit, not always clearly seen. One branched out system connects to another, sometimes to itself.

(hypothetically)
... A tree faporises water through all the leaves in the air, the condensed water rains above the soil in which that tree roots. The water is then absorbed back. (every person on earth inhails by every breath 2 oxygen-molecules that buddha ever inhailed)
So the end of the universe is clear, it branches back to a singularity when all black holes have sucked everything up and eat eachother.
But that may take for ever because if you look at the beginning, that singularity is like a trainrail in perspective. If you get closer to it, you become smaller, so you'll never reach it.
In the future when beeings become bigger (black holes form their atoms), the end won't come closer, because the blackholes only become bigger, but there is an infinite amount.
Where was I, it will collapse all, but there won't be life to see it happen. The best chance is to jump in a black hole. The universe-time will speed up to the end-collapse. You won't be ripped apart by the gravity, because the time-dilatation will make up for that, your stretched feet will wait for your head to catch up.
All the timelines will bundle again into one. So its a cosy fireworkshow. I'm sorry, the light is gone and you'll be smashed to smithereens by stuff that wants to jump in your black hole to.
Stay here, it saves you time and trouble and a headache.

This is a lot like my post but mine doesn't include the time paradox. You would never be able to kill John-18 as John-22 because you would never grow up to kill yourself.

This makes me think that "time travel" is only possible if time is n-dimensional (n>1)

Relatively speaking, anything could be considered as the truth until proved otherwise...
That is my own understanding of the n-dimensional where n>1..
The n-dimensional is the environment of the possibilities where only one outcome will configure in the real space-time, according to ones own position.

The only relation or connection that I can see between the concept of "time" and the "n-dimensional" is none whatsoever.
If you ask me the n-dimensional exists off time and space..:)
I consider it the kernel of existence.
The imagination exists there, and it, the n-dimensional, can be considered through the imagination..

For example; this our own real connection through this replies is borne out of that n-dimensional but the time tag attached only when in the real space-time.

Hypothetically, what I meant in my previous post that you commented at, is that, if put on the way you looking at it now, then the accuracy or the ability of the mind "seeing" or experiencing the future could depend on the capability of the mind dealing with the n-dimensional.
Bigger the factor of "n" that a mind can handle, more possible for it to make a 22 fit on the 18..

I could have actually made a big mess here..:)
Sorry if that the case..:)
Only imagination after all..:)

cheers