No, BMV do not control passports the US postal services provides this service. Passport renewal service are handled direct with your state department, you need to have completed form DS-82 (on line) or if its early enough you can do this by mail if you are unsure and time is critical call your state department and let them know of your situation and they will tell you your options .
I do believe so but I think you also need a birth certificate to prove citizenship and proof of address like a couple bills?? Not in stone but I think, you can call them, they are great people, I know them pretty good.
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