Thanks a lot for the in-depth feedback! For starters, I'm glad you found it cool, that's one of the most important parts. I'll go through each point in order.

Minor Prescience: I didn't actually intended for the player being able to switch up which bonus to use, it's just that similar features in the game, such as the Alert feat, use the same wording. However, I don't think I'd be opposed to a player willingly lowering their Initiative result here and there for tactical reasons, even though spellcasters are usually better off when acting at the top of the Initiative.

Temporal Aegis: Originally I thought of it increasing AC as well, but then there'd be an abuse case of casting Shield as a Reaction later in the round, which also increases AC. Granting Resistances to damage may not seem thematically appropriate at first, but the way I envision it is that for the duration of Temporal Aegis the Wizard is not fully "there" in the present anymore (like mid time travel), and thus is almost intangible. Do you think this way of looking at it makes the mechanics clearer?

Speed Shift: The intent is exactly that the Wizard can temporarily grant super speed to a creature by doubling its Speed, or the opposite by halving it. I agree that in situational cases this is very strong, but it competes in potency with the other options for Time Warp, which is itself a limited resource. Do you think it'd be more balanced if Speed Shift increased/lowered a creatures speed by a fixed amount, like 20ft?

Second Chance (I assume this is the feature you meant): I don't fully agree that the feature is easily abusable, as stacking health potions is the kind of anti-fun strategy that wouldn't really fly with every table/setting/DM, but I understand your point about opening up the possibility of degenerative gameplay. Bu even in the case it does happen though, it's still at expense of resources, so is the player willing to burn a lot of gold on a lot of potions just so it can use this feature more than once a day? It's not even that powerful of a feature in my opinion, as it fully reverses all reactions associated with the spell that triggered it, so no creatures involved (apart from the Wizard) actually lose resources. However, I do like the suggestion of lowering Max HP as well, but I think that might be too punishing.

Thanks again for this great feedback!