x10 on using the 4-1/2" grinder. MORE RPMs and the blades are designed to cut wet or dry (see package) and a bit cheaper than a diamond blade for a circ saw.
You don't get it. RPM isn't what cuts. SFM is. The speed that the diamonds pass over a surface is the same. You must spin a 4 1/2" disc faster to have the same linear cutting speed as a 7 1/4" disc.
Also, the larger circumference of a circular saw blade will make it last that much longer, and takes that much more diamonds. Hence the proportionately higher price.
Stick with the circular saw blade for straight cuts (or do what I do, and get a 14" demolition saw for this, but don't spend that for just one job).
I've done this before on 4" thick granite, but it would work the same on the thin stuff too. I have an inexpensive 7 1/4" circular saw with a cheap Husky diamond blade that I use with a small stream of water. There is no dust this way and that saw cuts full depth through granite with EASE! Now, I caught some flak last time so I will mention this- always make sure you are using a GFCI cicuit!
Don't do that.
Wet cut blades (with a continuous rim) must be wet to cut. And I mean really wet. Way to wet to use with any old electric saw.
A -little- water, just makes mud in the cut, and slows your cut drastically down, as the diamonds have to push through the peanut buttery paste of caked up dust. When sufficiently wet, a proper wet saw uses water to keep the slurry in the cut sufficiently thin, that things cut faster (my diamond routers actually shoot water out from the surface of the cutting tools).
Turbo blades cut wet or dry. I suggest one of these for a beginner, and DRY cutting.
Segmented blades cut ONLY dry. Both a segmented blade, and a turbo blade, are designed to bring air into the cut, and to use air to remove the cut stone.
Just wear a dust mask, and keep in mind where the saw will be throwing the dust, before you make your wife's car look like it was in a volcano.
Put the stone on a flat piece of grass, and cut it there. If it is at all unsupported, it will break near the end of the cut, under its own weight, and will NOT break where you want/expect it to. Granite is just like that.
As for anchors in the stone. Yeah, you can drill and epoxy them in, but you're concentrating stress, and asking for trouble.
I would epoxy a sheet of plywood to the underside of the stone, and anchor to that if that suits your needs.