Advice on cutting melamine I can help you with. I recently completed our kitchen reno and that's what I built every new cabinet with. (We went from 6 cabinets to 21. Whew.) The 'bad news' is, if I knew now what I knew then, I would have built it all out of MDF. What a nice wood to build from. Anyway, back to you.
My personal experience with cutting melamine relies on two things: a sharp saw blade and painter's tape. First, measure where you want your cuts. Then, lay painter's tape (the 2" width variety is best, imho) along the lines where you are planning on cutting. Using a sharp pencil, draw your cuts on the tape. Regardless of whether you're using a table saw, jigsaw, or router, make certain you have a sharp blade. Make your cuts along the tape line, and when removing the tape, pull it perpendicular (at a 90 degree angle) to the cut line, and in the direction of the wood. (Not towards the 'empty space' that you just cut away.)
I have found that using this method, you can achieve good cuts, with minimal chipping to the wood.