You ask some very good questions.
The police shouldn't be an issue no matter what plates you have as long as you don't get stupid.
Something to remember is that no matter where the vehicle is plated, all of the paperwork must be absolutely correct, along with your papers. If anything happens and you need to use insurance, the first thing they check is that all of the paperwork is perfect. You must be a resident to register a Mexican vehicle, and be sure to read about the legality of who can drive it.
Insurance is important, not expensive. We had to use it once, we were hit, not us hitting someone, and again, first thing was to make sure that everything was perfect paperwork wise. No insurance? If there is an injury, it's straight to jail.
Stealth camping around the magic cities? There are always Pemex and many will let you park there.
We seriously toured the country for many years, 15 years in a 22 foot 1975 Class C then upgraded for the last 7 (before we moved here permanently) in a 28 foot 2005 Class A. Honestly, no difference as to issues.
Facebook Marketplace is the place, at least in Guerrero, to shop for a vehicle.
Other members should have a lot of great information to share.