You are mixing up two distinct things r.u.s.s., 1) time travel and 2) parallel universes; maybe they are connected in ways we can't even imagine. The true is, none of us know enough about this to be able to draw a decent conclusion, all we can do is speculate.
I don't believe in that time paradox thing and how it could make the universe collapse; if someone ever invents a time machine, that's probably being a part of what is supposed to happen; if that person travels to the past and does something there which even terminates his own existence, then maybe that was what was supposed to happen, and the line of time will adapt - maybe someone else in the new time line invents the same machine and travels back to do the same thing. Even the smallest change in the past could have catastrophic consequences in the present - just imagine a time traveller taking one of our "modern" diseases (like for example aids) and spreading it 200 years ago.
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