We installed Pergo Select and it was the glued type. Didn't know it came as a snap-together type also. Check on this.
You want a glued type in a kitchen or you may have a disaster if it gets wet.
Almost all of the cuts you make will be covered with quarter round or some other trim around the edges. So a jig saw would work if you cut from the back side. It will chew up a lot of blades! See if you can get some carbide grit blades.
I have a 12" compound mitersaw and used up a couple of its carbide blades in doing our place.
The slab cracks are of no consequence. Seal them with teh same caulk you use for the edge of the Pergo. I used a clear 50 year latex caulk.
To clean the junk off the floor, get an 8" razor floor scraper. It is not easy but it goes fast and does a good job.
For a lot more tips on laying laminate, read that topic on my website at www.bobf.info.