I have a feeling a hawk had something to do with you losing so many of those kings.
But yes Kings do come in other colors besides white They could also be mixes, with runts, homers, or just about anything else. They'll fly around the house and loft, up in some trees, peck around on the ground...
No, giant homers are a show breed. Kings often look very similar to homers, just bigger. They'll fly around the yard a bit but you can't release them and expect them to come back from a distance.
The pigeons they sell for food are almost always King pigeons, in which yes, you can let them out after a couple weeks. That gives them time to get used to the place and on a feeding schedule.