A:AnswerYes. I have a glass screen protector on mine and it fits great. The grip case doesn't push against the screen protector, so the case won't peel it off.
A:AnswerYes. It does in general. I have about medium sized hands, so I can't speak to larger hands, but I definitely feel it helps with hand/thumb cramping compared to not having it.
A:AnswerI would say that for the most part yes it does. I know that after a while the controllers can get loose but when my console is in the grip the controllers don’t move unless I’m being a bit rough due to a hectic part in a game or something. I know that without it my controllers would probably just slide right off.
A:AnswerStrongly recommend screen covers and protective cases! The part that has caused the most trouble is where the controllers slide off and on the sides.
A:AnswerI'm using the HORI Official Nintendo Switch Go Pack Sling Bag Shoulder Pack - Mario Edition and the game grip and switch fit nicely inside with a little extra room to spare. I can also take my charger, cable and headphones in the same pack. There is not much room for anything else but if you leave the headphones out (or use earbuds) you can take a couple of Joy Cons and those small square game holder boxes in the extra compartment.