What can I be allowed to do as a engineering/ maintenance intern at a european airline?
In europe the MRO are regulated by Part 145, this part precise that you have to be  Certifying staff (owner of part 66) to work on aircraft. 
For all other people you can't even loose a bolt except if you are under supervision of qualified Certifying staff.

For engineering work (without work on aircraft) you only need to have a sufficient degree (under company appreciation except for special works like airworthiness where this in precised in concerned regulation (Part M for example)).