I did have a GA account waaaay back in the day, and as you can tell, I have ten little critters. However, one of them I plan on letting go, but I'm worried if I do I can't adopt again. Since I now no longer have a GA account, can I still pound one pet and adopt another to still have ten pets, or am I unable to do so now?

No, I don't think so. If five of your pet slots are from a GA, if you pound one, you will need to get a GA again to be able to fill the slot.

Aaaah, okay!