Canthan Quests

If I move my Tyrian char to Cantha, can I do the quest before Kaineng Center?

There is nothing before Kaineng.

yes there is stuff before Kaineng its called the shin jhi island where the monstary and stuff is and no you can't do the quests or anything from there

Besides the two missions, and of course the Dragon Festival stuff...

You cannot do the quests, but you can do the missions for Protector title credit, as well as map the area.