I have two questions please about the buses, a, we need to know bus number from station to residencia san niccolo and b, if train goes early from florence to pisa for flight home, we need to be at pisa airport by nine am.
you can catch the ATAF (orange colored buses) number 23, it will go right in front of the residence. (you can even see the bus number 23 making the turn on the Google Maps!!)
But I catch the bus in that area and I can tell you it runs very regularly, about every 15 - 20 minutes. Let the driver know where you are going and hang around up in the front of the bus for the first time - and he/she should be able to give you a good indication of where to get off.
As per going back to Pisa, you should look at the buses (they will deliver you directly to the airport and are easy to use) they pick up at the Santa Maria Novella train station out front (whereas the bus you pick up to go to the residence is on the side) and they sell the tickets both online or at the bus stop.