1. Theatrical rarities losing it in the end? The opposite. Curtain raisers.
2. Accountant spies flowering tree. Acacia. This is presumably accountant (ac) plus spies (cia) but that leaves me with an extraneous a!
3. Corps to stop honking tank? One's doubtful. Sceptic. Presumably septic (tank) around c (corps) but what does the sword 'honking' in the clue signify.
4, Whimsical name for ship. HMS Pinafore.