When I group something and go to another costume and then come back, the thing I just grouped is now ungrouped. Did anyone experience this glitch?

If you draw something else in the costume after you group something, it should work fine. It probably has to do with the file not saving changes for whatever reason after you group objects, but by adding something to the costume, you're activating the process of saving the costume, therefore everything you did to the costume would get saved properly.