Read the manual...ooops, nevermind, manual is of NO use. 
1 Crystals are a resource, like farms and gold that pops up when you've researched enough (I think it's in Adventure tree).
2 Every time you cast a summons spell, it uses one of your "Enchantment" slots. These are found when you click on the spellcaster in one of the tabs next to Actions, Vitals, and then Enchantments.
3 You can't "miss" that research. It's one of the first in Diplomacy. You either haven't researched Diplomacy, or you've already built the maximum limit of Caravans per city (it's 1 at the beginning,later tech allows more).
4. that level is related to your Adventuring research, though I can't be more specific about which path within adventure (something to do with exploration).
Hope that helps and sorry the manual is so crap.. it just is. Some links (like the Wiki) are trying to help with that.