Additionally the country lanes down the sea coast where all marked "Private property, tidholx"
If this is legal, than I don't know what is not!
The big question is - was it correct to give permission for that sort of building in that area?
Likely this replaced an older building, but still, it seems that aesthetics in consideration of the construction blending with it's surroundings is something that Mepa have no idea about as yet.
As far as the "no entry" signs go, fact is that probably the majority of open space in Malta and Gozo is privately owned or leased, including the roads thereupon, and as such it is not easy to say where one does and does not have a right to enter.
This does not exclude the possibility however that landowners without the right to the roads, arbitrarily decided to put up "no entry" signs on the basis that they take their chances with whoever decides to respect the signs or otherwise.