"I don't know how the counters are secured to the cabinets. "

Gravity and sometimes some caulk/silicone.

It is more just to hold them in place while joints are made.

The slabs are more than heavy enough to stay put (short of large overhangs) especially after the sections are joined together.

You do not need to do much of anything to the cabinets.

Depends on the thickness of the granite slabs. The 3cm thick slabs I think can hold up with little support. The 2cm slabs are usually installed over a 5/8" plywood base. You would need to check with your local stone suppliers to see which thickness is available in your area, or what's available in the color granite you want to use.

"The 2cm slabs are usually installed over a 5/8" plywood base. "

Usually supplied by the granite installers.

They mount the plywood, then the thinner stone.