To answer your questions:
1. Yes. You have an ICAO PPL.
2. You will be liited to day VFR unless you can rent a N-reg ac, then you will be able to fly within your licence privileges.
3. Go to a flying club, fly some sort of acceptance check, rent, fly...
4. It's a lot more expensive. The weather is less certain and RT is very different! Europe also has 'landing fees'........