When I'm doing tactics puzzles using the puzzle trainer, I often find myself drawing arrows and circles to mark things such as important squares, forks, pins, etc.
Since in real chess, there are no such markings to be made, will this hurt my chess and my ability to improve?
Of course, try to do puzzles without any assistance (just by thinking). It will help you ! :).
I've actually never thought of doing that. I think that might be a helpful beginning step to draw a bunch of arrows and such to answer questions from the board...are their pins batteries, etc. That might get you into a habit of looking for things like that and answering those questions when you're not drawing arrows. I don't think there's anything wrong with that at all as a stepping stone. That's my noob thoughts.
Probably not, but with an actual chess board you have to do it mentally.
Any solving of puzzles will help your game. You will benefit more from not using the markings, obviously, since you will have to be using the same techniques to analyze the board as you would while actually playing.
That doesn't mean you shouldn't use the markings if you need them. But like training wheels, stop using them when you can to improve your game.
