Can I work on my projects (self-employed) while visiting another country? [duplicate]

For most countries, the answer is no, a non-citizen cannot work there legally unless they apply for and receive an explicit permission to work in the given country. That might take form of a specific visa type, work permit, work-study program, endorsement etc.

There are exceptions, most notably the EU (a citizen of any EU country can work in any other), but they're uncommon.

That said, very few places prioritize catching and punishing people who take care of some of their business online while staying there for a few months. As long as you keep a low profile, don't tell anyone and don't do business directly with the locals, you should be fine. However, if you live somewhere for several years or get into trouble, at some point you might get questioned about where your income comes from.

Tax questions are almost impossible to answer without getting into many details about your unique situation. Generally, I wouldn't worry about local income taxes if staying somewhere under 6 months per year, but don't take this as definitive advice. Note that US citizens need to file taxes with the IRS even for income earned outside the US, but there are certain exemptions available.