check your contract, you might not own the code and your organization may have a process to determine how to license something.
to your other questions (IANAL)
prior work wont be licensed, meaning no one but the owner of the work is allowed to do anything with versions prior to the license
you don't have to, but i can't see a reason why you should not.
GPL might mean that other work depending on gpl licensed code has to be licensed in a gpl compatible way, depending on how exactly you depend on it and how you distribute your dependencies. MIT/BSD is easier here, if you don't plan to license everything with the GPL anyway.
check your contract, you might not own the code and your organization may have a process to determine how to license something.
Good point. I will need to double check the contract, but I believe the ownership restriction has more to do with patents and commercialization. All our output was in general meant to be made public.