Nuke Ships

I haven't nuked ships directly however they did suffer damages when they were next to the coast at a target I hit.Also keep in mind Cruisers have AA guns,if there are a few high level ones in a stack it might shoot down your nuclear bombers.And it's only a nuclear rocket that can be shot down with a rocket fighter.

Experienced players will be able to explain it better.

I've not done it myself, but if you press on the info button on a nuke, it gives you a damage rating against ships and I cannot think of any reason why couldn't. If the ship was moving it may miss, I have experienced that problems with flying bombs and rockets.

I have. They die. Of course you can.