When you leave a tile containing a "monster" blight, you have to fight or evade.
No you don't. If you end your turn at tile containing a monster blight you need to fight or evade. They don't mind you leaving. See [10.3] in the rulebook.
Does the same thing happen if you leave the tile containing the necromancer, therefore losing a life or grace if you don't have a holy relic?
See [8.2] in the rulebook:
A hero can battle the Necromancer directly under two circumstances: the hero can initiate combat with an attack action, or the Necromancer can initiate combat during the hero’s event phase if his secrecy is zero (see 4.1 − Event).
No, Necromancer won't punch you if you leave his space.