So, three questions:
1) Playing the first Shadow Magic quest (not the tutorial) my hero Oakleaf has died for the second time. I cast Resurrect Hero from the World Map and I'm told "No hero will answer your call" or something similar. What's the deal?

2) When and how do I use disjunction? I tried to use it to remove nasty spells the enemy cast on my towns but it doesn't seem to do anything, or even have a valid target.

3) How does Disjunction differ from Dispel Magic, and what sort of 'abilities' can Dispel Magic remove? Can you give some examples?

Thanks!

Resurrect picks a semi random (alignment play a part IIRC) dead hero to resurrect. Not sure why it would fail, though.

Disjunction is not used against local spells, but is used to try to dispel other wizards' global spells that turn up in the list of active spells in the Magic Options window. In fact you need to target the specific spell you want to negate from this window. It will work (if succesful) against anything from Enchant Weapon on an enemy Hero, to the all encompassing Mastery spells.
But note that if the enemy has also cast Spell Ward, then Disjunction will not work against other global spells; you will have to Disjunct the Spell Ward first.

Dispel Magic is a combat spell that tries to remove spells cast on a single enemy unit. The AI very rarely buffs their own units, so the spell is rather redundant in single player maps, although the AI can use it against you.
So Dispel is a cheaper way of removing an enemy hero's buff and it will try to remove all
the buffs, while Disjunction can only target a single buff. But the caveat is that you need to face that target in combat first.

BTW, it's always a good idea to check each new turn if new Global Spells from other wizards turn up in the Magic Options window.

I am not sure if Dispel Magic can only be used in battle? I think you can use it on the world map as well, on a specific unit. Quite effective.

Indeed, I recall the onte time my superhero, who was maxed out 20/20 on all, drowned when the AI casted dispel magic on him, dispelling the water walking enchantment.

One of the few occassions where I felt truly humiliated by the AI :)

Ah, yes! Now I remember that it is also a global spell. :-)
Been a few years since last time I played.

Whoever's got resurrection trait can't be ressurected again, I think.

Thanks for you help everybody - I think I understand now!