Flooring Tile - cutting granite counter tops

we purchased a used kitchen that includes granite counter tops. We have fit all the cabinets in the space we have now we need to set the countertops. The pieces are all straight. I need to know:
- if we can cut the countertop ( reduce the length of the piece)
-what type of glue to use to set the countertops
-what type of glue to use to join the 2 cut pcs together
I understand the cabinets need to be perfectly level.
We have a variety of heavy duty construction tools available to us.

Thanx

Granite can be cut with skillsaw with diamond edge blade. To prevent chipping you may want to collar the blade. Check the tool department for these giant washers that fit on both sides of the blade. These stop blade vibration that causes chipping.

Silicone caulk is used to attach counter to cabinets. 2-part epoxy can be used to seal seams. Color pigment mixed with resin before you add hardener will give you a color match for the granite. Check the paint department at your local home center for pigment kit. You can't make seams totally disappear, but that's what sets natural stone apart from man-made products.

Once the counter is installed, keep sealed with sealer recommended for natural stone. Clean and maintain with products recommended for natural stone.

Thank you for your help. I appreciate the time you took to answer my thread