How to shake off an agro without Invisibility?
Confusion potion.
Or if you're using Bake Kitsunes' or Command Undead you can get things to aggro your followers (providing they are attacking) by having the monster walk on to the same tile as the followers while you remain adjacent (if you move away the monster will re-aggro you and move off of the same tile as followers).
How to kill something big without direct damage spells?
What is the rest of the template and what are you defining as 'big'?
How to heal controlled undeads?
They heal themselves as they damage monsters.
You can also use JOAT Gift Of Renewal... otherwise depends on the rest of the template. Typically if you're using any kind of follower/pet to do the attacking you would either have a way of healing it, or you take the hits yourself with the pets added on for extra damage. Such as a Vamp Form/Dexxer/Tamer.
Not sure there's really a purpose for being focused spec Necro in PvM.