If coinbase decided to close my account for gambling or some other reason, will I be able to withdraw my funds before they close my account?
No,your account would suspended without the warning as per their terms and conditions which you "Agreed To" while signing up.
Yes,Absolutely correct.I'm also coinbase user but I've well much knowledge about there policy as the reason still I'm using it safe without facing any difficulty.Though I have a close friend who have faced this same problem and in end he lost his 50$ worth of bitcoin.Be alart always when you are using coinbase.
I'm not sure of this but I also thought this was true, the fact is that coinbase is creating pretty rare situations, most likely they will simply suspend your account and not give and funding back.