Do pigeons eat honeybees?

Can I raise pigeons in the same barnyard as my beehives? Do they eats bees?

Can I raise free range pigeons without hawks and owls completely wiping them out?

birds and bees as a general rule don't go together but the squab (pigeon) is closely related to the dove and neither eat a lot of bugs.
Pigeons usually are kept in a coop, so unless your pigeon house has flowers blooming in it, bees will tend to stay away, wasps on the other hand will likely see it as a good place to build a nest.

Hawks tend to grab more pigeons than owls will and unless you have a "safe haven" for the pigeons to roost in, the hawks will see them as fair game and an easy meal when they are out foraging.
This doesn't mean the hawks will get everyone of the pigeons, but they could make a fair dent in your flock.
That is why most pigeon keepers have their birds indoors most of the time.

Around here, there are plenty of free range pigeons that reproduce faster than predators can eat them. A key seems to be to have plenty of nesting sites high up around the eves of a barn.

When I kept pigeons, it was rare to lose a bird. I only released them from their pen for a few hours in the evening. Then they'd re-enter the pen through a one-way door. That worked great, until a new family member brought a cat with her, and it entered the coop through the one-way door and killed every bird.

Thanks! I can't keep them at my house in town. My land is about ten miles away, so I only get out there once or twice a week. I wouldn't want them in a pen. I think I may try some next spring.  There are feral pigeons near my house but probably less predators here in town.

I thought about building a coup inside the peak of the barn roof. It'd basically be a elevated chicken wire pen, but they could come and goes as they please.  There aren't any mature trees within 100-200 yards. I'm not sure if that helps or hurts or doesn't matter. Our conservation department used to cut trees out of the prairies to elimate roosts for predator birds. This was to save the prairie chickens. I don't know if it helped.

The nearest trees are pines. I don't think hawks or owls would use them.

It seems like a pigeon could out fly an owl?