In addition to the great answers above:
#3 There are 6 ways to obtain new spells. These are, from most to least common:
- The 6 Spellbooks; Air, Earth, Fire, Water, Life, Death. You can pick spellbooks at the start of the game and most heroes start with one or two. Also, the Decalon trait allows you to research and buy all Spellbooks. All, except Death/Life, because they are mutually exclusive. All spellbooks have 5 levels of spells.
- The Mage path traits. These include Summoning spells and various other groups of spells you can pick at level-up.
- Research the 'Magic' tree. Some of the most powerful Strategic spells can be found here. Some spells are Kingdom/Empire only.
- Some faction traits grant your faction some unique spells. Magnar and Resoln each have such a spell trait. Also, some races grant a racial ability that's very similar to a spell.
- Quests: a few quests grant you a spell. I only ever had the useless 'alchemy' spell, but rumors are, there's actually a useful spell to be had.
- Unique heroes with unique spells. Keep your fingers crossed and hope for a cool hero each time you reach a Fame threshold. At 200 and 400, there's a solid chance you'll get a hero with an unique ability. Some of the best heroes are quest rewards, so quest as much as you can!