OK, I'll take a shot here. The Gallery in 2.1 automatically syncs with your Picasa gallery. To turn off that sync you can uncheck the Picasa web album account from Menu > Settings > Accounts & sync > Gmail account. To delete the pictures, you can just touch the picture, touch the physical Menu button that shows up in the bottom right of the screen and then select delete. That should do it!
You actually cannot delete the photos (delete does not come up as an option when you select the photos), but turning off the Picasa sync automatically deleted the whole album. Thank you, thank you, thank you!
I more wanted to know how to delete individual pictures as opposed to just removing the shortcut in my gallery to them. I don't understand why the standard delete function doesn't exist that won't just delete that picture from the online storage. Sure would be handy.