No, there was no such champion neither in the World Cup nor in the Euros which didn't concede at least one goal during the tournament.
Even in pre 1976 Euros when championship basically consisted of a semifinal and a final game, champions would always concede at least a single goal.
The best result so far can be attributed to Spain during Euro 2012 when they ...
You're seeing how many challenges they have left (well, how many incorrect challenges they have left) in the set. See for example this RadioTimes article:
Players are given unlimited opportunities to challenge a call in each set at Wimbledon.
However, once three incorrect challenges are made, that player can’t challenge again until the next set.
If the set ...