If they have green leaves on them they are not dead. However they are damaged.

Of course they are not dead. Looks like they both need staking. Have they been hit by a lawnmower? Tumbling kids?

Just bought the house. Not sure what happened. Notice the hole at the base of the 3rd pic. What could cause that?

The first one in particular looks just like somebody drove all the way over it with a machine. With them both having a lean further supporting the idea that they were driven over, then came partway back up.

As far as replacement suggestions goes what specific features are you looking for?

Hard to tell but that last pic almost looks like there was a curve in the trunk they wanted to hide and planted it too deep.

tj