1-1/2 in. Zinc-Plated Wall/Ceiling Mount Pulley

The screw holes diameter for this Wall/Ceiling Mount Pulley is approximately 0.259 inches.

The pin for this Wall/Ceiling Mount Pulley is approximately 1.38 inches long.

Steel

The pulley will accommodate up to 3/8" braided nylon rope.

Yes

The wall / ceiling mount pulley should be able to hang the canopy from the ceiling, as long as the cable’s working load limit is more or less similar to the pulley.

The diameter of the center pin is 1/4." I just measured it. I would imagine that a 1/4" 20 bolt would work, but I'd shy away from a galvanized one as they are slightly thicker from the galvanization process. I'd recommend that you not tighten the nut to much as compression could interfere with the wheel's ability to rotate. Instead, allow me to suggest the use of something like Loctite thread locker to keep the 1/4"-20 nut on and it one place with only mild compression, or using two adjacent 1/4"- 20 nuts to keep the bolt in place, replacing the functionality of the product's factory cotter pin. Good luck.

Zinc plating is rarely sufficient for exposed outdoor use. For corrosion resistant coating like zinc is inexpensive. Also outdoors depending on the type of weather especially in the winter (Florida or Alaska type of thing). If rust gets a hold of it pretty bad, like in Florida it will last you a couple of years before it locks (so keep it lubricated).

I would use a 3/8 or 1/2 inch eye screw to hang a swinging chair.

I would suggest that you remove the cotter pin and pulley wheel. Then everything is very easy to bolt it where you want to. Then just replace the pulley wheel and cotter pin.