Idk about California but here in Iowa, and all of the Midwest, and pretty sure everywhere, no CDL is needed for your 4 bullet points unless you are doing it commercially. As in, if you are getting paid to do it, or “for hire”. Those bulletpoints are the same for all of the United States. I can tow my 14,000 camper anywhere I want and not need a CDL. If someone pays me to tow their 14,000# camper somewhere, then I would need to have a CDL, and a DOT number on the truck. Now of course, if I got pulled over by DOT I would just say I’m doing a buddy a favor. But if you are doing things like that all the time and/or using it for work, then yes you would need a CDL and you’d have to have a DOT number and register the truck for commercial use.
Farmers can drive a semi and grain trailer and haul their own grain without a CDL, because they’re using it privately and non-commercially and hauling their own stuff.