1. No age limits that I know of
2. I would say self-sponsor - you've got the GI BIll - it is generally much quicker to get into the academy self-sponsored.
3. Every dept will be different about the swim test. Some don't have a swim test at all - others require it.
4. Each dept will be different. State agencies and counties will be FRS(State retirement). Some municipal departments also participate in FRS. The rest of the municipalities will generally have a city pension plan.
5. You may get "veterans preference" points during testing at some departments. Some departments also allow you to "buy back" prior military service - time that would go towards your pension - again - each department would be different.
This isn't Burger King, you are not going to get it your way.