They are plays on words. "Warship envy" is a play on the expression "penis envy", and (in a similar vein) "warship waving" is a play on "willie waving" - where a "willie" is a BrE pseudonym for the penis. "Willie waving" means an ostentatious (but generally false) show of strength/toughness/aggression/manliness.
Your understanding of the meanings of the various sentences is correct.
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