OK - answer from she who knows.

Nearside and offside come from horse riding. Nearside is the horse’s left hand side. This is the side of the horse you would normally get on and off from. This is probably down to the fact that most people are right handed. Because you get on and off a horse on the animal’s left side, that is where the mounting block (or pavement) would be, and this is why we drive on the side of the road we do*.

Offside just means the other side of the horse.

I have no idea why other countries drive on the other side.

I am sure it was something to do with shaking off the shackles of colonial oppression. Most countries have of course at some point been part of the British Empire

You are quite correct redflamesThe old jag was a tourer and had 2 x 12 gallon tanks i cannot remember which one though, had a Customer who "ran" out of petrol cos he did't know where the changover tap was
and it had nothing to do with horses it was to do with having right hand free to draw your sword, thats why a lady was always on a mans left, except if you were a Kerr in the borders as they were all left handed and the spiral stairs in their castles were the opposite to a normal stair