Can you use skylanders giants on the new swap force?
yes, in a review done by Good Game on their Good Game SP show, they showed a clip of one of the Giants approaching one of the 2 elemental gates and showing so that would mean it's possible however it seems just from the review the game is designed just for Swap Force characters with a lot of area's locked even for the basic character
Good Game SP - Skylanders Swap Force Review
Yes, Swap Force is backward-compatible with all figures from the previous games: Skylanders Spyro's Adventure and Skylanders Giants.
Giants are not necessary to complete Swap Force.