Nomading since 2012.
Most of the issues you raise vary quite a bit from one location to the next. For example visas depend on (a) the country you have a passport from, (b) the rules of the destination country, which will probably have multiple visas available with different requirements, (c) how long you need/want to stay. Every country (and sometimes every bank or even branch) has its own rules for opening accounts -- sometimes easy, sometimes not, and usually not necessary if you only intend to stay for a short time.
Health care access and costs also vary widely depending on where you go, what kind of insurance you have, how much you can spend, etc. Multiple companies offer short-term travel insurance geared to nomads, and multiple companies offer expat policies with longer and usually better coverage (CIGNA, Aetna, etc.). US medical insurance generally not accepted outside of the US (but find out). Other national health insurance may or may not cover citizens outside the home country, you have to research that.
Taxes depend on your country of nationality (where you have a passport from) and the destination country. In general people traveling on tourist visas don't pay income taxes in the countries they visit (because they are not legally allowed to work there), but increasingly countries offer remote worker visas that may include paying local taxes. Most countries tax their citizens based on time spent in the home country, but the US (almost uniquely in the world) taxes US citizens regardless of where they live, and on all income regardless of source. In my experience most nomads don't pay taxes in their destination countries, and only worry about taxes imposed by their home country. Taxation of expats and nomads changes as countries either try to attract or crack down on remote workers, you have to research and maybe get professional advice if you have tax questions.
Remote workers with full-time jobs have to either inform their employer, or try to hide their remote location from their employer. Employees working in another country, legally or illegally, can present tax and labor law compliance problems to the employer. Some companies cannot permit employees to work from foreign countries for compliance, privacy, or other legal and regulatory reasons. Don't put your employer in a bad position by deceiving them, that could cause a lot of trouble for you.
Nomads overcome the challenges by preparing in advance as much as possible, doing the research, and learning to adapt and figure things out. Inflexible and judgmental people who think the world should work the way they want it to don't succeed as digital nomads. Those who can adapt, adjust, and not get overwhelmed by bureaucracy and cultural differences succeed.
While remote work/nomading is always new to people who haven't done it, or just started, the issues are fairly well understood and written about at this point. NomadList, for example, has free information for many destinations, and an active community of nomads and expats who can answer questions. Reddit used to have a lively digital nomad forum, I haven't looked recently. No matter what you read in a blog or see in a video or get told in a forum, do your own research so you aren't stuck with bad information at some foreign immigration office, or your health insurance doesn't get accepted, or your bank blocks your debit card.