1. Yes, there are multiple opportunities with most everyone you can encounter as of v1.44.1
2. Funnily enough the photo of the Nurse seems to have been printed off your smartphone... You just have to catch her in a compromising situation either during "Loser to the Rescue" or "Photogenic"
3. It really depends on what sort of person you would like to be. For me personally I'm quite partial to more vanilla wholesome stuff so I usually go after Flora or Lindsey. If you don't like anyone you meet in the first couple days you could always hold out on the romancing until Season 2 and go after Maya, though there isn't anywhere near as much stuff for her yet. If you like a good mystery there are also quite a number of hidden secrets around the school...