Is it cheating if i start learning about an opening once i see an opponent use it.


No.
in a daily game, you are allowed to have access to books.
A lesson offers you general guidelines about positions. It cannot possibly cover every move.

I did that halfway through a game, and my opponent flat out just said that I should have already started doing so when the game started.


No, in Daily Games it's not cheating unless you look at the computer evaluation of certain moves/positions.

What is the "circle of trust"? Is it just some way of saying that you shouldn't do anything even close to cheating? As long as you are not asking an AI for help to learn, I don't see what is wrong with it.

@RurikAunimoto ... The Philosophy of "Circle of Trust" club is what you are not allowed to do at standard OTB tournament do not do it online. Call us chess Romantics. :cool

Check the rules of the site before calling something cheating by definition. https://support.chess.com/en/articles/8583921-what-counts-as-cheating-on-chess-com

Imagine in OTB game your opponent pauses the game to watch a Youtube video about the opening you're playing
Imagine in OTB game your opponent pauses the game to watch a Youtube video about the opening you're playing
It's not an OTB game. Correspondence chess rules are clearly defined. The resources that are allowed increase the quality of the games played.