How to wire three 10W LED spotlights to one plug?
Yes, that would work.

Use a 3A fuse, unless those lights have a terrible efficiency your power draw will be less than 1/4A. There will be no issues with the cables ability to handle the current.

No it won't have any effect on brightness.

That said I would advice against your plan. This is almost certainly against any electrical safety codes, they would require 3 separate plugs.
That terminal block is going to have 220V on it and most terminal blocks aren't designed to be safe if left laying around where people can reach.

Assuming the cables aren't too thick it would be safer to wire all three directly into the same plug. 
Failing that at the very least ensure that the terminal block is one of the ones inside a housing to prevent any accidental contact with the live connections.