Installing a laminate countertop on uneven cabinets

The only other reason I've used them is to create a consistent reveal- notice the distance between the bottom of one drawer and the top of the next? Now compare that to the top of the top drawer and the bottom of the countertop. The eye likes to see symmetry.

Do you actually need them? No.

While I am not a cabinet maker by trade, I have successfully built two full sets of cabinets (base and uppers) and am currently getting ready to hang my third in my newly renovated kitchen.

First, always start with the corner box. If it is not already level, square and secure, you'll want to make it so before attaching the other boxes as it's your foundation.

For #1: Yes, you will clamp the front frames together to align and level them to the corner box. Then secure them to the wall using #2 answer below. Then you need to attach the frames together as that will keep your seam from becoming a gap. Your screws need to be 90 degrees not angled when you screw the cabinets together. Do not glue, you may want to replace or refurbish later. You can easily hide the screws by counter sinking your screws 1/2 inch or so and using a plastic or wood plug. Or simply use a nice brass finish screw to compliment your woodwork. Or use a screw that blends in with the color of the wood if you are really concerned about it. Since your cabinets will be painted simply paint the screw head if it is even visible.

For #2: In all of my cabinets I have built a 1 x 2 solid wood rail at the top and bottom of the back of the cabinet that the 1/4 inch panel is nailed. I use this to attach the cabinets to the wall studs for base and upper cabinets. I use 3 inch drywall screws. You do not need to secure to the floor unless you are creating an island that does not have wall access.

I have not tried them, but you can also purchase rails in 8 foot lengths that you can hang on the wall, then attach brackets to your cabinets that hang on the rail. This secures the top of the cabinet but I'm guessing you'd still need to fasten the bottom through a stud.