Hi eddm, welcome to RA!
Sorry for the late response, I'll try to answer your questions:
1. Can you accomplish work with just a pressure pot (as opposed to getting the vacuum set up as well for degassing)?
You can, but you will need to design your moulds very carefully to ensure there are no air pockets. For best results we now only recommend the vacuum and pressure combination (you can use the same pressure pot for both functions). Pressure can crush small air bubbles but not large air pockets. So long as the mould was either degassed OR cured under pressure you won't get dimples.
2. California Air Tools - yay or nay? This seems to be the company I'm going to side with for an aircompressor and a pressure pot.
Unfortunately I'm not familiar with that company, so the best you can do is read reviews online. Cheap compressors are all pretty much the same so it's hard to go really wrong there. The compressor you linked to looks good - the main thing when choosing a compressor is not the flow rate (CFM) but the tank size.
Their pressure pot looks great, so I think is worth trying. Construction is a bit more solid looking than cheapo pots.
3. Would the two tools above be compatible/good for the job? In my newbiness, all I know to make sure is that the compressor can supply enough PSI, and the tank can handle more than needed to cast (40-60).
Yeah I think they would be a good starting combo.
4. What's this TCP supply company, and how are their pots?
No idea. The first one you linked to is overkill with the agitator. The second one is just a generic cheap pot, the same as many of us have. Mine looks very similar. Is it better than the dreaded Harbour Freight pressure pots? There's no way to tell without maybe measuring the metal thickness. It's certainly an appealing price...
Hope that helps!