So when a card reads:

"Reaction: After an enemy fate card resolves (or similarly "After winning an edge battle"), put this unit into play rom your hand as a participating unit on your side."...

Does this mean I can play it without paying for its resource requirement? Or do I still have to pay?

Put into play and play are defined in the rules on page 13.

If an effect allows you to put a card into play, then you do not pay its cost. If an effect allows you to play a card (such as Backstabber or Ackbar), you do pay the cost. As Toqtamish says, this distinction can be found on pg 13.

Right on. I never got a rulebook in my set, and the store I got the set from refused to do anything about it.

But I'll be getting a second core set soon, from another store.

We can help out with that as well:

The game's support page has a pdf copy of the rule book that you can download (as well as a pretty good FAQ).

FFG is also pretty good about replacing defective or missing parts, you can go to More > Customer Service along the top navigation (or here) .