Argentina explains their digital nomad policy. About no Argentina taxes if working remote, and how to extend after tourist visa ends. Now giving $500 USD tourism coupon if stay longer than 3 weeks [1]. This seems to be something new
Yes, of course there are. You may or may not be able to work remotely on a tourist visa, depending on the country and duration of stay. You may or may not be required to pay taxes where you're working, depending on country. You may or may not be able to do your job there, depending on country (does your job require using data that is regulated in some way? Does your employer have policies regarding data residence?).
It sounds like fun. You'll find a bunch of info if you Google the term "digital nomad".
I've never been clear how many people are actually doing it, or how the economics work out. (I think it depends on the exchange rate of the country you're going to.) And of course, living in a foreign countries has its own challenges. Choose wisely.
I don't see why you would need a visa, you are a US citizen working a job in the US. There could be some fun with your taxes depending how long you are out of the country but nothing major, mainly if you try to use your being out of the country to avoid paying taxes.
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The loophole is not telling anyone. People love to make a big deal out of location, but if you can have a remote job and keep the hours they're looking for, just do it, don't tell immigration in the counties you enter, and don't tell your company, and there will be no issue. Otherwise you risk wasting a bunch of time on paperwork for no reason just to satisfy some bureaucrats need to be involved.