I wish you the best of luck for both you and your fiance! My husband and I were already married before bootcamp (for a year and a bit) and I met another woman who married her husband 2 weeks before he left for bootcamp. Having the BAH (Basic Allowance for Housing) is extremely helpful, especially since the woman and I met and I both live in California where the rent is insane.
If you're worried about it, you can get married on the Friday of his graduation. Great Lakes is lovely and I'm sure the city would be able to accommodate a wedding. My husband's recruiter married his wife between A school and C school, as they often get a week "break" between there. (No guarantee).
I dug up my DEERS form and have a website for you, it's to help find the nearest DEERS office after you get married. https://www.dmdc.osd.mil/rsl/
You'll also be given this information when the time comes, but I personally stress out less with more information. Feel free to take a look and see what's in your area as well as Pensacola. It does not have to be a Navy branch! I did mine at the Coast Guard base, as it was the closest to me.
Now to try and answer your last questions. The chances of being stationed overseas is unknown. It's possible, my husband and I want to be stationed overseas and are hopeful for it personally. If he does really well in A school, he might have a better chance of getting stationed in USA. Once you get married, your fiance will be the one that gets you moved to his orders. I believe he has to submit a chit to move you. There is more information out there about that, my husband is in A school currently at Great Lakes but I won't be joining him as I'm trying to finish my bachelors. Now, for your last question. Your chances of not being able to move with him because you aren't married is very possible. That is the scary reality. They won't really want him to live off base (every A school has their rules).
If you have any more questions or concerns, I'm still new, but I'll try my best to help you out! Best of luck to you and your fiance!
You will not have time to get married in Great Lakes at his graduation. Lake County, IL has a 24 hour waiting period after getting the marriage license, and he will be at the airport by then.
I wish I got to read this post early on....I am in the same situation as you. I have been with mine for 7 years and he left on 9/13. He is also an E-3 PACT. You probably will not have the time to get married at Great Lakes. I feel the same fear as you do, but the only thing you can do is trust your partner and support him as much as you can. You can probably get married once things have settled and go from there.
Best of luck to you and your sailor.