Relationship between the puzzle's rating and the player's skill

Recently I focused on the puzzles, so my puzzle rating has increased significantly. I got to 2000 puzzle elo and I started to wonder what those 2000 elo mean. My personal elo is something between 900-1150 at the moment, so I have some questions from this point.

1. Is that a usual thing, that I am able to solve quite fast and (mostly) correctly a 2000 elo puzzles?
2. Is there any dependency between player's elo and puzzle rating (e.g you should be able to complete puzzle rated on twice of your elo, or x1.5 of your elo)?
3. Does solving puzzles that focus mainly on checkmates, pawn races or winning trades (it is like 90% of things I get) have some impact on the real game?
4. If it has, how big that impact is?
5. Should I focus on some other things like openings or lessons if I can't climb higher in the standards games?

Thanks in advance for any replies.