Can I complete quests for a game I already play?

To answer the question in the title; yes. Using your current accounts, though, isn't too much of an option. Giving that the quests don't require you to play too far into the game I recommend registering and just playing on a new account to do them. That's what I did anyways.

No you can't

You can complete quests for a game you have already played, but not with your current account unless you created a new character under that account(option for some games). If that's not possible, then you'll have to create a new account, either way, you have to start from scratch each time.

Hello VayneMainIRemain__O_O_II
I reckon you will need a new account to do the quest but since you play them you should be able to speed through them!