Help me understand the sexual shenanigans in 'Singin in the Rain'

This is a weird film full of hinted at relationships. Help me untangle the web. Here's what I've worked out do far:

Don Lockwood is a famous silent film star whose ostensible beau is his film partner Lina Lamont. In reality of course she's his beard and his real lover is fellow hoofer Cosmo Brown. Early in the film Don meets Kathy Selden, in whom he recognises a real fag-hag. He resolves to introduce her to Cosmo.
Meanwhile Lina is having a torrid and sexual relationship with the owner of Monumental Studios R.F. Simpson. She has got her way through prodigious amounts of sexual and emotional blackmail with him, even threatening to reveal Don's real life to the newspapers if he doesn't fulfill her every demand.
Kathy does her best to save Don and Cosmo's relationship but realises she can only manage this by getting rid of Lina. Plus Don introduces her to Simpson who promptly falls for her. He confesses his troubles to Kathy one night in bed, and promises her parts in upcomoming projects if she helps him. Now Kathy's resolve is strengthened, Lina must be ruined.
During the film we see the fantasies obsessing Don's mind: rough sex with mobsters and Latin vamps, being a young hoofer all ready to be taken advantage of once again.

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