Welcome to Grouvee!
These are all good questions. It kind of goes along with this recent thread: When do you consider a game to be properly “played”?
I actually built the “played” shelf as a combo completed/dropped/done with kind of shelf. In my mind, if I had played a game in any capacity, it just belonged on the played shelf. I also built in play through tracking so you can indicate if you’ve finished a game and when. I’m actually just now building filters for the shelves to let you filter your collection/any shelf to show what games you’ve completed.
If I had to do it over again, I’d probably split the played shelf into completed/dropped (although that still has its problems when it comes to endless games). I can definitely see not wanting to put a game on the played shelf that you quit because you didn’t like. It’d actually be nice for recommendations to have a dropped shelf too. People would be able to see if a game gets dropped a lot, or you could even build some kind of engine that analyzes what type of gamer drops certain games and recommend to someone what not to play.
I don’t know, as I type all this out, maybe it is worth considering adding a dropped shelf as a core shelf.
I think you’re spot on with the idea behind all the other shelves though. Ultimately, it’s up to you to use them however you want. No ones going to get mad at you for doing it your own way 
Hope you enjoy Grouvee!