It's Pet Evolution, Baby!

[ransamaru]

must wear an egg obtained from monster after the event starts? or may carry on pet that become evo stage 2?

[SoulCrow]

I don't think it can be pink versions of the pet. Since its not mentioned.
I think you can do that from a different character so long as you have a level 75 character in your account on the server you raised your pet.
As mentioned above;

"Players much have a character of AT LEAST level 75 on the server the pet is raised on to be eligible for rewards"

must wear an egg obtained from monster after the event starts? or may carry on pet that become evo stage 2?

I think you need to have it new when maintenance ended. since if it was evolve already it won't count