I haven't grown pomegranates, but I'd guess it's an issue of ripeness. I'd say that second problem would be that the pomegranate wasn't ripe (or maybe overripe? I don't have experience to say which, but I'd lean towards underripe).

I've read that splitting is a sign that they are ripe ... though of course birds and all are going to raid those split fruit, so I believe the splitting is natural, but maybe catch them before they are that split? I bet if those are ripe, those that set at a similar time are just about ready, too, so you could try picking and opening one. It could also be a watering issue, though; I know a lot of fruit develop splits and cracks if watering is uneven.

What location? Anyway prune and fertilize next spring

It's in the back of my backyard. The wall is on it's north and west side. So it's facing towards my south and east side.

Should I prune off the fruit that has been split and eaten?

And where is the backyard? Country, State/Province, Big City ... hardiness zone?

It is in Las Vegas Nevada. Zone 9 A I believe.