Wow, interesting replies and ideas... I think it all boils down to ones beliefs about what time is and how it works.
I personally believe time as we know it is a straight line and obviously goes only forwards. I don't see time as something that revolves around humans but vice versa. Tomorrow is going to always be tomorrow, however the things we do and who we are may change tomorrow. I don't think a split timeline is something that could happen since that would imply that time revolves around actions of each individual.
With that in mind, I think that if time machine was invented in a persons lifetime who lost a leg in the past, that person would have to put the effort to travel back and stop themselves from losing a leg. Just thinking about doing it will not get his leg back. The moment he travels back and does enough to stop themselves in the past from losing a leg, he disappear from the past and never exist in the form and with memories he traveled back with. Puff! Gone!
So I guess option 1 for me...







