Yes, they would be half-siblings.
Yes, you can breed them. Having different moms increases genetic diversity but also makes dad more prepotent. It's very common in the horse world, esp. Arabians, to breed half-siblings.
I would if the sire is something you want to perpetuate (ie his dam was a great milker, he has good conformation, fast growth). And for a lot of people, this is the only option they have.