1. Are they all the same sort of being?
I'd imagine that the categories are fairly "mutable" at the upper levels of power in the Dresdenverse. Odin/Kringle can be Fae, or not, depending on what Mantle he's using right now. Mother Winter is one of the Queens of Faerie, but she has iron teeth.
"Titan" might just mean "a being of god-class power older than the better-known pantheons".
2. What is the relationship they have to the Angels?
Well, I'd imagine that all the really powerful and ancient beings are at least somewhat familiar with one another. They've had eons.
6. Did the Greek Titans (Cronus, Atlas, Hyperion etc) rule the world once? How did the new gods (Olympians) defeat them? It seems understandable just how much of a threat they were.
Well, mythologically, the Olympians had the aid of the Hecatoncheires (Hundred-Handed Ones) who were imprisoned by Ouranos, and (IIRC) freed by Zeus. And the three original Cyclopes (not the ones like Polyphemus from the Odyssey) made Zeus's thunderbolts. Both Hecatoncheires and Cyclopes were siblings of the Titans.
7. Does every culture have Titans?
Probably not
every culture, just the ones that have a myth of a war between generations of deities like the Olympians/Titans or Tuatha/Fomorians.