Can you apply for a re-entry permit at any immigration office in Thailand?

Do it at the airport. 1200 baht, they do everything - forms and photos. Takes about 15 mins. Just before Immigration at Swampy, after immigration at DM. The signs pointing the way are so obvious you can't miss them

If you have tourist visa stamp/tourism extension, you can apply for re-entry permit at any immigration office (but may need TM30).

If you have Non-imm based extension, you most likely need to go to the immigration office where issued your extension.

In either case, you can apply for re-entry permit at the international departure airport when you leave Thailand no problem.