find some useful trivia from strangers on the internet... but at some point you will need solid legal information -- from people in authority with real names.
I suspect that the state in which you register your boat will have the info you need.
We have lots of "out-of-state" owership boats in our state, and if you needed info on how registration works just contact our Marine Board. State of Oregon: Oregon State Marine Board
I betcha all states have some similar source of info.
Since we have no sales or use tax, the whole process is relatively simple here, in any case.
As an example, my total cost to register my 34' sailboat here runs about $110. for two years. In Euros, that's probably pennies.
The Marine Board has quite a good FAQ on their site, and they have always been courteous and helpful when I have called on the phone. If you have a fancy cell phone account it might be a free call.
As to your other question about visiting other countries -- here in the NW we find that Canada treats state registered boats with no prejudice, being as there are thousands of them visiting their waters every year (and spending money.)
Everyone I know that has gone south to Mexico or Central America advises having a vessel federally documented
because other countries do not recognize our state decals... and what with there being so many different ones I can understand why. So, if you own a boat and are not a US citizen, that's a whole 'nother kettle of fish you would have to resolve. US Customs and the USCG probably have information on their web sites about this.