There are alot of variables in play here, have you consulted a professional for this project?

Slide in range would work the best. You could always go with a cook top and put the stove the wall units on another wall. Budget and resources will dictate your choice.

I agree. A slide will do fine. Some have the knobs in the front and it's easy to bump them and change the heat setting. Look for one that has the knobs slightly up and shielded like the Fridgidaire GLGS389FS or something similar. All stoves should be vented to the outside.

My comment above was based on whether there would be an elevated snack bar, (i.e. a wall to separate the countertops and support the overhang). Or a single piece of granite with a 30" cutout, and a 12" or better over hang unsupported. In the second example there should be a pony wall for support.