I very much like the World Bank idea; the International Court and Security Council also sound quite good, but for sake of variety it might be worth avoiding repeating bonuses from the existing projects. Similar for a Eurovision equivalent.
Thus, my suggestions for effects would be something like
World Bank: similar to what you have. Perhaps one level might increase gold from Trading Posts?
International Court:
1st: receive the power to propose an extra resolution at each council.
2nd/3rd: not certain what to do without repeating rewards. Most likely happiness and culture boosts.
Security Council:
would use a mixture of the bonuses from your SC and WWG. +10XP doesn't sound like much, though; perhaps all units receive a particular promotion (Foreign Lands bonus - "Peacekeeping Missions"?) One reward might be a bonus for either Barracks/Armouries/Military Academies or for Walls/Castles/etc - I'd suggest a culture boost, but there are a number of things you could do with that.
Music Contest: a few suggestions. Really, I'd prefer to get a bit away from bonuses purely to GMus, but the obvious alternatives - Tourism boosts, Happiness boosts - have largely been taken already.
1: Concert Tours are +50% more effective
2: Free Great Musician (perhaps more than one?)
3: +25% generation of Great Musicians
I don't think that rewarding winners with increased delegate numbers is a problem providing a limited number of nations get the delegates. Similar to World Ideology or World Religion.