Hey, give us time! I just got on line today!
I know you are hurting, and bobby too. I'm so sorry, and to have such a sudden and unexpected loss seems to make it even worse in my opinion.
As far as your questions, I think Bobby knows. He may be doing what the rest of us do and try to coax her into not being dead, but he knows. I'd say you can safely take her little body away now.
I'd say if your heart can handle it, get a companion for Pepper going right away. Quarantine is going to take some time, so there's no need to stretch it out further than necessary for the lonely fellow. I wouldn't worry about appearance; the fact that the new bird will speak budgie will be sufficient.
Either male or female will do, and if you have a male, they will be bestest friends without worrying about egg laying and any inherent risks in that activity.
I know this is a sad day, and you have my sympathies.