I've never done the regions mentioned, but (assuming VFR; the man said "PPL") the way ICAO flight plan distribution works is that the ATCU where the FP enters the system gets out a big thick book of addresses, and addresses the FP to various relevant ATS units en route, according to waypoints which you specified in the FP. You must have at least one waypoint in each country's airspace. Occassionally they get it wrong...
You are then expected to report by radio as you go along.
There may be a theoretical ICAO privilege to fly non-radio in Class E/F/G but in reality once one gets away from the "civilised" places they fully expect constant radio contact, so they will tell you to call the next frequency.
There are plenty of old grey pilots consuming beer in airport bars who will say otherwise, but they are probably thinking of the Humphrey Bogart movie era.
I know a certain amount about how IFR flight plans are distributed in Europe but know nothing outside that.
Overflight permits is something else, and people I know tend to use a commercial outfit where you pay some $$$ and they get the permissions for you.
Avgas is likely to be the most fun of all. I've looked at some long distance fly-outs where a bunch of people go off to some bongo-bongo land, and they either use local knowledge to make sure the stuff will be there, or they get avgas shipped out in advance, in drums. This is a very good reason for flying a turboprop.