Paradoxes are not possible because time, as a whole, isn't linear. That is just how our senses perceive it in 3 dimensional space. Each time line is personal and relative to the observer. "Time as a whole" is more like an infinitely dense tangled web.
I travel forward in a linear manner to kill my father in the past. The "me" that would have been born isn't actually the same me as the traveler, the traveler continues on through time in a linear manner the world forming around them.
Once you start to travel away from your original time line you can never get back. (I should actually say "more generic time line", because you never leave your own personal time line)
It appears to be a many worlds universe but on the larger scale it is not, everything that was or will be... is.