Hi, back, and merry Christmas :) If this is a subplot, I'm almost afraid to ask what your mainplot is... :P I think that kind of challenge would be a great idea! Do you have a suggestion?
I'd suggest that before you think of any of these details you should give more thought to how time traveling works in your story. What you can and can't do are the most important things you should work on. There's a system to everything, and creating one for time traveling would give you a...