You can build reputation daily by setting school policies that parents approve of. You can avoid losing reputation in random events if you make sure the inhibition of the general community isn't too much higher than the inhibition of your students.
At the start of the game relaxed clothing is the least inhibited option that you can go without triggering hit to rep and NPCs will see your principal's undies when evaluating your rep. Dress up your principal properly. School policies impact rep too.
You see hearts only for friendship and relationship. NPC attraction is based on multiple stats and high friendship won't help to do weird stuff with NPC that has low corruption, low loyalty, inhibition and age difference. "Hearts" are rounded decimal numbers in those stats. "I have a lot of hearts" means nothing as you can see up to ten and thresholds for passing some actions require specific stat value or some thing that is not calculated in hearts.
Flirting allows to improve friendship with NPCs, but you can't repeat some actions and best choices depend on NPC personality. It is a lot easier to increase friendship with gifts to around four hearts, get their phone and then raise friendship to the max with small talk over the phone. With some special NPCs you can get phone via moderate relationship level somewhere around six hearts. You will not get any "weird" events and pictures by flirting with NPCs. Flirting is game mechanic that you use only to learn what it does and then you won't bother spending your time on it.
! means that character has ongoing quest. Generic friendship affecting actions are restricted on such characters.
