Residential Rent Agreement

I rent a parking space in SF (rent controlled) and I wonder if it is subjected to the same rent-controlled apartment laws as a dwelling?

Not at all. Rent control only applies to residential housing, and not to parking spaces.

No

I seriously doubt it. But you talk about San Francisco. Legislators to enact legislation that city rather strange all the time. Ask your councilor to push for a right of the parking space rent-controlled. Your wish could be granted.