Antonio,
My answers are mostly my opinion, but hopefully they will help:
1) The Cluster could be a component (using the component 3d box widget). In the component you would have the machines, and inside the machines you have your app servers. Conceptually correct? May not 100% UML compliant 100%? No idea. But it would help show how it works. You could do something non compliant, like use a dotted box to represent what's part of your cluster. As long as it conveys the clear intention, I would say it's correct.
You could have only the app servers inside the cluster, but from an UML kind of way, it's weird, because of overlapping boundaries. Is the machine part of cluster? Not exactly, but the cluster can't exist outside of some machines. This arises from trying to mix two a "logical" deployment and the "physical" deployment into a single diagram. I would still keep it to a single diagram, but understand that you're mixing somewhat separate concerns.
2) It depends, actually each server connects to the database. It's not the "cluster". However, in terms of the diagram, I find your sample pretty evident in what it tries to convey.
3) Yes, I did show it. It's important to show it. In one of the node machines? In a separate machine? Well, look at your NFRs to see what's more appropriate, but I don't think either one is really wrong.
Good luck,
Andres