1. Gallery shows whatever pictures are on the phone, iit doesn't have its own place to store them. (The album name is the name of the last folder in the path for those pictures.)
2. In order to delete files, the phone has to be rooted. (You can't get to th part of storage you need to get to without root.)
3. You'll need an app like
DiskDigger undelete (root). (The free version will undelete pictures - for other file types, you need the paid version.)
Warning - rooting and installing an app
can overwrite one or more of the files you're trying to recover.