1. How does it work with the flightplan over here filling is not the problem but were do you open and close your VFR flightplan? Because in the USA you do it at the FFS.
On controlled airports the controller (ATC,AFIS) will do. If flying from uncontrolled place, the first controller you will speak with.
2. How does it work if I want to fly from one country to another? I know I need to file a flight plan for that but how does it work with ATC communication and preparation.
It is easy, like this: "Vienna information, G-ABCD, 2 minutes before border, request handover" "G-ABCD contact Bratislava information 124,3 Good by"
Regarding preparation you will need sometimes cross the border at prescribed reporting points, in western Europe it is rare in my opinion. Sometimes the flightplan is required to contain the EET to the border. That's all provided you are within EU and Shengen.
3. How does it work with the landing fees?
You have to see the office at the airport (big black C) and there is somebody who will collect the money they are good at it
On big airports it is expensive, basically dozens EUR for landing and even more for mandatory handling, the cancer of GA.
In the sum it is not complicated, nor expensive if you pay attention before the flight. Just call or check the website of the airport.
In Europe the countries have sometimes different regulations like transition altitudes, night flying rules and so on... You have to check the AIP of the particular country. It is no big hassle, everything on the net.
Miroc