No, that isn't right. You have shore based duties(drafts), so wear the cap tally of whatever base you are working on. Portsmouth used to be HMS Victory as in the ship and barracks, but then it changed, so the barracks are HMS Nelson. There's also HMS Sultan in Portsmouth, and HMS Collingwood in...
Yes.
The other point is, even if the caller had mentioned a modern sea going ship, the fact that he was on the gangplank, meant it was still in harbour.