Some ideas are:
- You branch off into another timeline and your actions make no difference to the previous timeline
- You’ve already taken said actions but just didn’t know about it so nothing changes
- Actions taken can have an effect (so you could suddenly erase yourself if you killed your parents)
- Only “nexus” or fixed events really matter, the timeline will sort itself out for minor changes
- something else entirely
One timeline, actions can have an effect. But once you time travel you unmoor yourself from normal causality, so you could do things that should negate your existence and nothing will happen to you.
Indeed, if you time travel again you can’t affect your own actions anymore. Like, you travel back 20 minutes, do things for an hour, then jump back 5 minutes, when you go back the second time you can’t alter yourself. You could go later the you from before you ever time traveled though.