Can non-giant figures from Skylanders: Giants be used on Skylanders: Swap Force

They function more or less the same as in the first Skylanders game. The level you unlock is the same, and has the same storyline, but the gameplay might be a little different since they took the same level layout but used enemies from Sky: Giants instead of just using the enemies from Sky1. You can use it as a powerup item mid-level, although it might ask you if you want to play the Adventure level.

Yes, the figures are cross-platform compatible.

Make sure you buy your grandson a Starter Pack for his specific platform (either Skylanders Spyro's Adventure or Giants), and not a Booster Pack, both kinds include them game and figure(s) but only the starter pack includes the required portal of power.

The Spyro figurine isn't available for purchase by itself, the regular one was bundled with the console starter packs and Dark variant was bundled with the 3DS starter pack, but the Legendary variant is available in a Toys "R" Us exclusive bundle. Some figures that were only available in level packs or bundles for the first game are now available separately, so Spyro might be available on its own soon.