I personally only work term time but I think you can work out of term time
No. Post-doc work is like any other research job and it doesn't have 'school holidays'. However, the hours are relatively flexible. No one really cares what hours you work (any time between 8am and 8pm), as long as you get your work done.
Although, there is an extended shutdown period around Easter (a few extra days) and the department is shut between Christmas and new years.