Say I was to take my car and park it in some upscale neighborhood (non-private) and then live in my car, would this be illegal? Let’s say a I had an old RV that I parked (and didn’t move for months) and lived in? Could I be arrested? Forced to move on?
Yowie. I would think that it’s not illegal - but to the residents, it’d sure as heck be distasteful.
But the street isn’t the property of the residents - it’s public domain. So maybe a cop COULD expel you. I’d hope that they’d be more compassionate though. 
Many (not all) cities and towns have stringent restrictions on overnight and/or long-term parking. I lived in one suburb that did not allow trucks parked on the street overnight – much less an old RV. In some towns, police give stickers to the residents on a street and ticket everyone else. That usually happens where a residential street butts right up to the commercial zone.
It would depend on local ordinances.
If nothing else, what you describe sounds an awful lot like loitering to my non-lawyer ears.
You can have the living crap harassed out of you, as I discovered during a brief period upon which I do not care to elaborate. I was threatened with jail nightly, but never got vagged.
According to my less-than-friendly neighborhood officers, it is illegal to sleep in a car in Fairfax County, VA. It is also illegal to sleep on public property at night, and it is illegal to sleep on private property not your own. Moreover, you can’t sleep in a park during the day if you look like you didn’t sleep the night before. As best I can tell, it’s illegal to sleep in Fairfax County unless you can afford to live there, or perhaps more importantly, can look like you can afford to live there.
I remember seeing a documentary about an English couple who were unemployed and by some twist of paperwork couldn’t receive any sort of housing or benfits so were forced to live in their car. It was a programme that I couldn’t tell whether it was real or a spoof.