When I moved to Dubai, I declared myself non-resident in UK for tax purposes. Dubai was tax-free. Now I find myself resident in two countries for tax purposes and paying tax in both. But I've mixed feelings about it. I'm actually quite happy to pay taxes back in the UK, less keen on paying taxes in Australia, as they're rather scummy these days to NZ citizens, so I'm getting a little screwed over with no path to permanent residency, very little benefits, yet still have to pay full whack of tax... Lovely. (Fuck Australia)

But, in your situation, moving every 2-3 months can mean you might actually avoid tax residency in most countries. So it can be complex. Look into the three or five flags theory for perpetual travellers. Also into tax-residency rules of the countries you'll be staying in.

Essentially you want to have your citizenship somewhere where your foreign income is not taxed. Have a legal residence somewhere with low tax/tax haven. Earn your money/host your business somewhere with low corporate rates, have your assets somewhere where they aren't taxed massively and spend your money somewhere with low levels of consumption tax/VAT.

As for visas, it's really just travelling at a slower pace. While working remotely, it's kind of a blurry situation. Mostly though, as long as you don't remain longer than six months in one country, you're unlikely to fall foul of residency laws (for tax purposes).