It is also the EU Countries and Visas. Before I moved to Denmark I just assumed they'd just welcome Americans with money but you can't just have any job, you have to be paid by a Danish company, over a certain level or found a startup with very specific requirements, etc.
Danish immigration laws are also very strict. Most of our political parties have been competed to further tighten those rules over the last couple of decades. We literally have people advocating to leave the convention on human rights, since it’s getting in the way of that
French immigration is currently allowing remote workers on the one year visitor visa, so long as your company doesn't have a presence in France. Basically, as long as you are not doing business in France or taking a job from a local they are fine with it.
However, it's difficult to proceed to a residency permit in this situation, and you can't join the national healthcare system.
VPN. Simple as that. Most companies aren't bothering to check anyway, most that do aren't detecting VPNs, and for the few that do that, there are ways to circumvent detection if you are really determined.
Not if you set the VPN up on your router. You can also buy small portable routers designed specifically to sit between your machine and your wifi / ethernet.