No you can not get keys by leaving a Fireworks game. You have to play the full game(take not I may have misunderstood you here but I have no clue...). And never trust any statistics as those are just odds. It doesn't mean you will get one in every 5 games.
Honestly, to me, there is no one game that is best for getting keys. It's whether you are lucky one day or not. For instance I got 3 keys in shells in about the time span of 1 hour. I would normally only get one key or no keys in that time.
Also crates only appear in shells and NPCs. Keys appear across the NPCs and all of the games.