I would guess the hole diameter will be 3/16" but after you drill off the rivet head you will see the hole the shaft goes through and can just measure the diameter of it.
As for the depth range, once you have the rivet shaft out of the hole you can make a little depth gauge out of a paper clip wire with a short right angle bend in it, put in through the hole and get a pretty good estimate of the depth.
Pull-Up Strap Handle Kit
Classic Freestanding Rack
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