visualization
The best demonstration of visualisation is playing blindfolded chess. I can play games blindfolded agains beginners, hoping that they play a bad defence which I know well, like 1.e4 e4 2.Nf3 f6?! 3.Nxe5!? fxe5?? etc, and mostly I will checkmate them. However, if the game is not forced I get soon lost, and I need at least an empty physical board to go on playing.
I visualize in 2D since I majorly play online so I wouldn't know the proper advice to give for OTB. If by colour you mean the colour of the squares, then yes it is important or at least it helps. At first I had issues visualizing the colors of the squares and had to use an algorithm but I found that a bit unnatural. Luckily, most of my problems with diagonals and colours were fixed when I started visualizing the board in four quadrants, so maybe that may help you too.
That's actually a very good question. I'd like to hear a bunch of super GMs describe what they visualize in their mind's eye. From the little reading I've done, it's usually described as an abstract model of a board, but the explanation is usually extremely vague.
I've found that it helps to visualize a board full of living pieces...

... except with naked women.
...
...
Look at my rating, and then argue.
The best demonstration of visualisation is playing blindfolded chess. I can play games blindfolded agains beginners, hoping that they play a bad defence which I know well, like 1.e4 e4 2.Nf3 f6?! 3.Nxe5!? fxe5?? etc, and mostly I will checkmate them. However, if the game is not forced I get soon lost, and I need at least an empty physical board to go on playing.
You never actually visualise the board or peices, just chunks of abstract information. Ask any good blindfold player whether he sees in 2D or 3D and he will say neither
I said already above that people only visualise chunks, not whole positions. And concerning 2 or 3D: I found some IMs or GMs talking about using one or the other, or sometimes only an abstract “feeling” of a specific part of the board( which is what you are talking about, I guess). I began a new threat top to collect quotations about visualisation, check there what Axel Smith wrote on this subject.