I got actually a lvl 60 mage.
Can i lvl a new class somehow with the help of my mage, so it goes faster?

You get no xp as a lvl 20 if a lvl 60 kills lvl 60 mobs for you.
You get no xp if you got a shared quest with a lvl 60, even tho you completed it.

You DO however get xp from quests you have, even if the lvl 60 kills the quest mobs for you.

So that's the only possible way I could imagin right now.