Does the F5 LTM communicate to the pool members via ip address or DNS name?

you can do either if your version is semi recent. either add them as FQDNs or else just IP.

In the older F5 code versions, IP address is primarily used for pool members. You don't have to explicitly add a node. When you add a pool member, node is auto-created. I think you have to be on 12.x for dns name (not sure).