In my mind, a mitered edge is just that -- a miter rather than a butt joint. What you have now is just a rectangular piece of marble stuck to the bottom of your contertop. With the miter, they will cut back the edge of your counter at about 45 degrees. Then the piece that creates the built-up edge will also be cut to match that 45 degrees, and be attached. The seam will be the edge of the countertop itself -- not a visible seam along the middle of the edge piece. Now, color match is still an issue, but a mismatch won't be as obvious. If they used a piece from the same lot as the previous piece, you would see the darker top of your counter, and the white on the side -- still a mismatch, but not as obvious that it is two different pieces. I think it would probably look as though, when "sliced" the marble was dark on the outside and white on the inside. They still need to look for a better match.

The lip should never be in front of the top cabinet rail. That will make the cabinets look like that top rail is short if you cover part of it. You always use build up with a built up counter. That goes for laminate, or any mitered stone counter. The buildup strips on top of the cabinet edges support the counter. Or, if you are having custom cabinets made, you can do an extra tall top rail to all of the cabinets so that looks even for all of the rails.

I bet the cabinets are built in place. Moving/removing might destroy them. You may end up saving the doors and having new boxes made. Then they can be any height you want. The sink will be a problem if you don't replace/raise the window, too. You need that sink for the feel of the kitchen if you want to keep the look of the cabs. It will probably cost the same to just buy new cabinets. But that doesn't solve the sink problem in the same foot print. And if you change the foot print then you've opened a new can of worms. Changing the window size would probably be the best thing to do.

6cm is a very very heavy look, as is chiseled. Chiseled is also complicated by the fabric damage that it can cause. It's best used as a bar or buffet rather than a working counter. You can have clearance issues, unless the cabinets are planned for that from the beginning with your Kitchen Designer, as it will be taller than the average counter unless you choose custom cabinets. The trend has been towards a more modern look, with thinner counters. But, what's appropriate depends on the overall context of the design. The price is a bit modest for the work needed to upgrade the average kitchen to a 6 cm look.