Are we allowed to take the robot during or after a competition outside, say back at the school, to work on it?
No.
After a regional, you must directly ship the robot to the next regional. You may have the robot back once you’re done with all your regional/national event(s). However, there’s not much point to work on it then 
I’m not so sure there isn’t a point to work on it some more… Working more will allow you to perfect your 'bot, and you’ll probably learn a lot from it. It’ll help you spot design flaws the next season around before they happen.
And, if nothing else, it’ll give you something to tinker with. 
After the regional is a definite no-no… I am not too sure about during the competition… but I would also have to say no because that would give you an advantage over other teams who do not live near where the regional is being held 