You ask what spark plug gap means ? It's the gap between the end of the centre electrode and the side electrode so it's the gap the spark has to jump. I enlarged your pictures on my computer and it's obvious, from the first picture, that the gaps are all over the place.
Here are the plugs I took out of our Panda last time I serviced her and you can see the gaps are all the same and you can get an idea of what a correct gap looks like:
View attachment 216732
The Haynes manual is not very helpful stating that the gap is "preset" and, to be honest, I've not had a problem with plug gaps since they started boxing them up with that wee cardboard tube over the end, but if you want to check, a gap of around 30 thou (0.030") is a pretty good average setting.
From what you are telling us about your running problems coming on after the timing belt was changed, my bets would all be placed on the timing not having been been correctly carried out - by that I mean I think it's very likely the cam shaft and crankshaft are not correctly synchronized, maybe one or two teeth out?
As Jockcl500 says damage may have been done but also maybe not. If it were me I'd be getting the cambelt correctly fitted and than doing a compression check on the engine before making any decisions about taking the cylinder head off. If the compressions come up good then you've likely got away with it?
I have to say you do seem to be very unlucky with your choice of mechanic. Maybe third time lucky?