1. Just do the physical, and take the time to think about it after you actually get an offer. That's totally normal & acceptable. Don't go out of your way in the interview to say you will need time to consider this. Act really enthusiastic, but keep your eyes and ears open, then take time to process your impressions afterward. Don't worry about their cost of the physical. If they weren't willing to potentially eat the cost, they would not have scheduled it for right after your interview.
2. Not unreasonable, but potentially a deal-breaker on their end if they have no power to work the system. I was recently hired at a county system & was told they never, ever pay anyone's moving expenses. But my manager worked it so that we said my start date was a week earlier on paper than it was in real life. So I managed to get a week's pay for expenses. That's an exception. In many cases, libraries have no flexibility in the budget. Have you asked them about whether they can pay any expenses? If I were in your place, and I were flying out there to interview at my own expense, I would want to know ahead of time if there is a potential they could help pay for the move. If not, it sounds like you already know that is a requirement. What if they offer you the job but no moving expenses? Just wondering what your thought process has been on this.
3. If they wanted you to prepare any sort of presentation or portfolio, they would have asked you. That doesn't meant that if you have something ready to use as a handout after your interview you should leave it behind. I find it helpful to have career-related paperwork handy in an interview even if you don't use them every time. Definitely ok to ask how many people will be at the interview.
4. Smiling faces!
Look at how staff are dressed. Look at how busy people are. Look at the new book shelf. Browse the stacks, especially the children's area. It's bad enough to have musty old books for adults, but lack of weeding in the children's section is a
bad sign. See if you can see what public service staff are doing between helping patrons. Ask how long people have worked there -- that's always a good indicator of whether it's a positive environment.
