Here is a old (from about 2003) e-mail I wrote. Enjoy; It would be good to hear some comments on it. My opinions have changed a bit now but I stand by some of it.
I have just read your webpage 'Various Musings on Time Travel' (admittedly only once - I feel something like that should be read a few times). I thought that your analogy of a flip book for a 4th dimension was perfect: I could now explain 4 dimensions to a young teenager. I'm very surprised that you didn't carry it on for the rest of the discussion; especially on a multi-verse. As with any good article, most of the questions I had were answered or at least mentioned, and I'm left with more questions than I started with.
I have only one negative comment on your article, which is of determinism, you didn't seem to look into the consequence very much. Starting with a definition: I believe that the laws of nature are so strictly defined, that given all information about one point in time, and enough processing power, we could work out everything about the next instance in time. I also believe that to do such a thing is impossible . Thus we have the situation as follows: you have free-will: no one can predict what you will do, you fully believe that you can make any choice, AND that of determinism . Randomness is caused by everything we don't take into account when doing an experiment; hence there are still 'random' events.
SINGLE TIME LINE
In a world with only one timeline and assuming that we can go back in time - this will cause us to realise that we don't have free will. We cannot kill our father as we didn't: we can only do what has already happened. Hence, you cannot change the past. The reason that we haven't seen any of these changes (seen any time travellers) is that we haven built anything to receive the energy/mass (signal/traveller). No paradoxes, but then again no free will and no where near as much 'fun' as a multi-verse.
I didn't think that you covered the idea of physically not being able to make the decision. Not some strange co-incidence not letting it happen.
The stuff above I have thought through before, the stuff below has quite a lot more assumptions and flaws.
Let's describe a multi-verse: we have another dimension. We have the, infinite sized axes: x, y, and z of the 3d drawing on the page of the flipchart. We have all the infinite number of flipchart pages representing time. And we have an infinite number of these flipcharts that represent every universe in the multi-verse. A five dimensional space; infinite in all directions.
Movement through the first 3 dimensions is by transferral of energy, the 4th is mostly automatic (time travel changes this). Movement through the 5th, well lets look at one possibility that you didn't discuss.
We could move when ever something happens. For instance, a coin lands on heads, hence, we are in the universe where the coin landed on heads. By changing stuff we are simply moving to the flipchart where that happens (in the same way that we automatically move to a new instance in time). We are moving through the 5th dimension.
Determinism almost becomes a moot point in a multi-verse with time travel. We can predict what will happen in the universe that we are in, but we can move between universes so there is not a lot of point.
When we time travel to another universe we can change things; we can add and remove matter; kill the 'version' of our grandfather; whatever we want. But we are simply in the universe where that happened.
Thought experiment time. We have a time-mahcine that can freely move about in both the 4th and 5th dimension. Let's only look at 2 universes, A and B. We will look at them from 3 points of reference: from Bob's, from A's, and from B's. Each point of reference will be from the chronological order of the one perceiving it.
Bob is in A in 2050; he time travels so that he is in A in 2000. He kills his mother called Janet; hence he is in B in 2000. The act of killing brought about the change.
Bob's mother, Janet, gives birth to him in A in 2020. He time-travels out of this universe.
The Bob from A arrives in 2000, kills Janet, who is not his mother. Hence Janet does not give birth.
From here Bob can travel to A where his mother is alive or to B where the person he thinks is his mother never gave birth.
It's the same with telling yourself winning lottery numbers. The fact that information has travelled back in time will cause the movement to a new universe. The likelihood is that the movement of information will cause different numbers on the lottery machine so it it's not a lot better than guessing. The more chaotic a system the less accurately the information from time travel.
In essence you are using one universe to compute an approximation of the other one. The universe is almost the same (bar the information that travelled back) and you know what happened in the future of the very similar one.
VIOLATE LAWS OF NATURE
If there are an infinite number of dimensions, which cover everything happening, surely we can move to ones where the laws of nature don't apply. The only reason we haven't is that we cannot produce a situation where we violate them. If we produced them then we would be in such a place.
You are only able to think if you are alive. By thinking, you are in a universe where you are not dead. Hence, you will only be able to think in the universes where you didn't die and hence you will think that you are living forever. There will be some universes where you don't die and that's the only ones where you will perceive. Do something that will definitely kill you according to the current laws of physics. Does this mean that you will move to a universe which ignores the laws of physics? Shoot yourself in the head to find out.
Note that we might not be able to move through the 5th dimension very easily. It might take beings as long as it took them to create a time machine to create a 5th dimension machine, it may not be possible at all. If that is true then we have the case where we can kill our mother and live in a world where we no one gave birth to us. It's not a paradox if you say that the other universe exists but we can't get to it. The laws of conservation only apply to closed systems, we cannot observe all the other universes and hence we may gain matter and energy from other universes.
Note that the only difference between a universe and a multi-verse is the ability to move in the 5th dimension: something that can only be proved by time travel. I have removed most of the paradoxes you have described but only by defining things or assuming things. I haven't discovered anything.
My head is buzzing; every time I write about this stuff I come up with so many counter arguments to my thoughts that I find it hard to express anything of value. I hope you like my musings.
 My reasoning is that. We cannot build a computer fast enough to perfectly emulate (NOT estimate) itself and do other some stuff. Inside the universe (or even multi-verse) we cannot predict everything that will happen without dedicating the entire universe to working it out.
 I know that it is a leap-of-faith, but please, just follow the line of thinking.