For a situation where you see a classmate regularly every week who is a romantic interest (and have already gone on a date with), is it best to have good, lengthy conversations each time you see each other... or is it best to be brief with her such as (hey how's it going) and just chit chat for a few seconds, OR even further just not talk to her at all in class unless I'm trying to ask her out? Is this entirely irrelevant and I'm thinking too much about it or is there some importance to this?
Youre definitely overtinking it. If you ignore her, it's going to be weird. I'm assuming you guys did not bang on the date. So youre goal should be flirting during class and keeping the sexual tension high and than getting her on that second date and sealing the deal

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Well, you should somewhat put it into a 70(her to you)/30(you to her) ratio.
Start off with just talking back to her and not making the first move.
That's my humble experience with girls at work.