To buy more AA past the free 250 you have to either turn the account All Access or buy the Alternate Ability Increase which costs 250 daybreak cash for an increase of 100 aa. It can be found in the Market place under services.
Almost cheaper to go pay for one month $15 and then auto grant and get all the AA up to your level (you should be like level 80 when you do this).
Auto grants to 100 now. Which is about 10-12k ish AAs, depending on class. All-access required for that.
All Auto Grant does is give you AAs while you're an all access account. Once you revert to silver/free, you can keep the AAs you have but still not get more, so no more autogrant.
Yes you keep any AA you get or are awarded (from missions) or /earn/grant during the time you paid for the account. Make sure you spend them if you have extra since once you go back to free you cannot spend any extras you might have left over. You do not get to keep the J5 merc, the rank II spells, the ability to wear prestige or the loyalty velocity that goes with the gold accounts.
you can buy a fairly cheap item off the marketplace that allows you do use rank 2 spells even if silver/free.