I am Dutch, bought my boat in Greece, from a German owner through a Dutch broker. After I bought the boat I registered the boat in Poland, which is the easiest and cheapest way to register your boat. Poland is in the EU and in Schengen, so you won't have any problems there.
You do need insurance all over Europe, in fact marinas want to see a copy of the insurance whenever you check in. You may also have checks by the police while on the water and also they want to see an insurance. I know in the US the Coast Guard does most of the checks, but in Croatia and Greece you will mostly get visited by the police.
When it comes to licenses for the crew it is a bit of a complicated matter. Some countries demand specific local licenses if you don't have an ICC or RYA license. Croatia is one of those countries if you show up without a license. The local license is not difficult to get, used to be that you had to pass by the harbor master on Saturday morning, do a small exam and you would get your license, which is then only valid for Croatia. There is word that Croatia will now also go for a practical exam, but nothing final yet.
Other countries are more strict. E.g. the Netherlands don't require a license if the boat is less than 15 mtr or cannot go faster than 20 km/hr. But, you don't need to do a practical exam, it is just a theoretical exam, that is it. If your boat is longer than 15 mtr and / or can go faster than 20 km/hr you need a license. However, you will need to study for that exam, it is not an easy exam to pass. Most people take their courses in winter time and then do the exam in the spring. If they catch you on a boat that requires a license and you don't have one, that will be a fine.
As a foreigner you also need a license and for the larger boat that will be an ICC. I have both my Dutch license (which is equivalent to ICC) as the RYA Day Skipper license, plus radio operator license, so I can basically go wherever I want to go.
If you have an EPIRB on board you need a MARCOM B license as an operator. If you have a VHF on board you need both a license to have it on board plus a license to operate it. Both licenses will be checked by the police when they stop you.
As for insurance I have Pantaenius, which is an insurance that is widely used in Europe for boats. Of course there are others, you need to check them out. I don't know if you can have Pantaenius with a US registered boat.
Now the difficult part here is the Non EU citizenship. We do have Schengen and there are rules how long non EU citizens can stay in the Schengen area. Once you are in Schengen nobody will check whether you overstayed your allotted days. However, when you leave Schengen............that is the moment they will find out and that is the moment they can hand you a fine and tell you that you can't enter Schengen anymore for the next 5 or 10 years.
Some countries are more strict in that then others. Croatia is known to have no sense of humor, they have picked up foreigners from their houses, escorted them to the border and thrown them out. That has happened so don't expect to get away with simply overstaying. You may, but you may also not get away with it.
Croatia is also known for handing out fines if they see you going out of their territorial waters while you are tacking with a sailing yacht and then tacking back into the territorial waters. They will happily hand you fines for illegal exit and illegal entry of the country.
Greece even goes further. Lots of people come to Greece with their EU car, leave the car there during the summer and pick up the car when they go back home at the end of the summer. At that time there are a possible options. First one is that you get away without a problem, but it is also possible your car has been impounded by customs for being longer than 6 months in the country without importing it. Another option is that they catch you at the border and then you can get a fine of several thousand euros. So be careful with it.
