Your first and third scenario seem not to honor conservation laws, one can probably build some nasty consequences out of that. Or what happens to the matter occupying the space you are about to appear in, where does it go? In the third scenario it can not simply switch places with the matter from the future because that would kill the asymmetry of that scenario and provide a way to send stuff to the future. I was not simply talking about you killing your younger self. To have any real merits one has to analyze a time traveling scenario with the same mathematical rigor as our normal physical theories. But I never thought much about about time travel because it is such an hypothetical idea and therefore my example a probably pretty bad but I hope you get the idea of what I am aiming at.

Conservation laws are man made, if the underlying universe does not follow them then so be it.

As to other interactions their are a great many possibles but they don't mean much. For example restricting things so only light can move though time does not change the underlying options in terms of information and paradoxes.

PS: Mathematical rigor is again a human idea, our universe could be absolutely random and we would have no way of knowing. At best we can say that seems unlikely.

Well, we can also just say the same things about paradoxes of all types. Partially the point of science-fiction (and science/philosophy) is that our thought experiments have parameters consistent with our current knowledge of reality if no other restrictions are specified.