This is designed for saws, you might get it to attach to the rotary tool but be this is not its purpose. The rotary tool arbor might not work.
This should not be a problem. I used these to do a part of a glass tile backsplash. It sounds like the backsplash is already installed? If the backsplash is not installed just make sure you have it resting on something very flat to avoid cracking the whole backsplash. You can use a little water from a spray bottle if your saw does not have a wet saw attachment. Just enough to keep the cut wet - a little water can do a lot of cooling. If you have a scrap piece of backsplash, you should try doing a test cut just to be sure that if you do get any chipping, its something that you can cover.
Yes. It will work with any saw that accepts a 3" blade. I used this on my WORX 4" saw and it did the job nicely.
I used it on my cut off tool. I have the Dewalt XR Oscillating tool with quick release. The Oscillating tool goes back and forth not circular motion. I recommend a diamond Oscillating tool it works great for small cuts.
Granite countertops are usually either 20mm or 30mm. Depending on your grinder, you would be unlikely able to get through. I recommend a handheld wet saw.
Yes, the 49-94-3010 diamond blade cuts hardibacker and cement board, just don't try to push the saw too fast. The 49-94-3005 blade, which says it rated for fiber cement, drywall, and plastic, bogs the saw down too much when cutting hardibacker board.
No, a true 3/8" only.