Julian,
I cannot really answer your questions because I never had any problems of the sort you are concerned about. Nor have I heard of anyone having had such problems.
But that does not mean it cannot happen to you.
Only recently I heard that some guys got an inspection when going through Switzerland, but they said that was probably because their boat was so conspicuous and curious, a 28 ft. whaler, seldom seen between the Swiss Alps.
I would however always have a copy of the original invoice to hand, in order to be able to prove that VAT has been paid for the boat some way down the line.
As for your trailer and lighting, they seem to accept a british trailer, as long as it is not openly defective.
Safe travels,
Claus