I would hope so. Guess it depends on the deal that is made with the publishing company.
Nope. The publishing company, unless they specifically got movie/TV rights in the anthology contracts (unlikely) have nothing to do with it.
Whatever happens will depend entirely on the agreement the authors and Martin made with each other. For instance, the contract I worked out with my SWC buddies gave each of us certain shares depending on how early we had come into the anthology and giving me an extra share as editor. We bought Steve Libbey out when he was unable to continue, so should we sell media rights, we already have a method of dividing whatever we get up that was all pre-agreed to.
Whether or not Martin and his co-writers have that in place, I do not know, but I hope they were all smart enough to. Nothing sours a deal faster than an in-fight.