AFCI are designed to detect arcs, as indicated by the name. A brush type motor makes arcs. It's almost certain that your saw used a brush type motor, and the frig and a/c units may as well. I think you'll have trouble if you plan to leave those things on AFCI breakers. Things like lamps, electronics, and most heating pads don't normally generate arcs nor do they have brushes in their motors, so those things, more common in a bedroom, wouldn't create problems. It sounds like the breakers you have are doing what they were designed for, and tripping when detecting the arcs from those motors. Brands vary in their input circuits as to how sensitive they are, and whether they detect that the arc is dangerous or not and likely to overheat things and start a fire (which is why they were legislated).
If you could run the frig and a/c units off dedicated circuits, or move them elsewhere other than circuits protected by AFCI temporarily, I think you'll probably find the problem goes away.