"nerd girl" Is that what you call Violet, you barbarian?
When it comes to meeting the cast, you have to do the extracurricular things - studying, mingling, training, etc. You aren't guaranteed to meet a girl and get her respective event through it every time, but if you do it enough, like for studying, you'll meet Elisabeth and Violet, and go through their respective event lines. While when it comes to the trial, what were you doing? Trying to brute force? For stats like spellpower iirc, you could use animal form to skip a part, while if you want to at least meet two of the girls and pass, just max out knowledge, if you read the options, and can deduce which one accompany's the knowledge stat, you'll be able to breeze through it as first place and the exams.