Breastmilk storage and usage questions

Hi! 35 weeks with baby number 2 and trying to get as ready as possible. I will have 12 weeks of leave, but want to try to build a freeze stash as I work 12 hour shifts and it will be hard to pump. 2 questions:

1) if I pump at work and store the milk in my cooler bag that’s in a fridge can I freeze it once I get home? Or can I only store it in the fridge?

2) if baby only eats part of a bottle that was warmed from the fridge, how long is it good for sitting at room temp?