A: yes, but you should pre-drill with small drill bit and hit the wood lathe. Follow with a drywall slightly larger in thickness of the bit. This will prevent the wood lathe from splitting. May take 2 attempts because of the gaps between the wood lathe. If that is impossible, use a toggle bolt and secure with a butterfly. Follow instructions on package. This will be the strongest anchor for the hook.
A: They are small and you can see from the size of the screw. They are quite strong and I use 2 of these hooks with toggle bolts to secure them to the wall to hang mirrors in excess of 50lbs.
A: The dimensions given in the specs are likely the size of the package:-) The screws look more like 1" to 1.5" long, just from the picture