Memorizing the board I'm always experiencing difficulties while trying to visualize what moves a tutorial (or an answer here for that matter) is talking about unless I have a chessboard with coordinates nearby. 

Is this something I should fix, or is it fine to be using a chessboard? and what can you advise someone who want to memorize it?
The easiest way to visualize the board is to practice!  I know that sounds trite, but there aren't really all that many shortcuts.  Go over games in magazines.  Start from one of the positions given as an image and then "make" as many moves as you can in your head.  Try to see the position and look for the threats and ideas of each move.  If you can only make one move, that's fine - it's a good start.  

Similarly, you can use a physical board when you're going over a game.  Play out the moves on the board and start to learn the squares by name as opposed to figuring out which square is which each time.  That's probably the first step.  After you know the "names" of the squares, the rest will start to fall into place.