At least when I calculate, in general, I'm only looking at a particular area. Maybe less than a quadrant, and maybe half the board or more, but rarely is it the whole board.
I usually only do a whole board visualization at the very end of a line, to check how much, if any, compensation the side losing material might have.
Although before trying to solve a puzzle, I will familiarize myself with the position by looking at all the pieces. Maybe a rook on a1 doesn't seem useful now, but I need to know it's there because it may be part of the solution. So even before calculating I recommend looking at each individual non-pawn and tracing its line of movement with your eyes (even if it's through pieces). For example a rook on a1 you'd look across the first rank all the way to h1 and then from a1 up all the way to a8 no matter how many pieces are in between.
Hello! I am new at chess (relatively), and have started to do tactic puzzles on various websites. I have heard good players visualize the puzzle and (after finding candidate moves) run through the variations in their head. Do you guys only visualize the pieces that are of use, or all the pieces? Doesn't memorizing where all the pieces are first take a lot of time? Thanks