this came up in a story about the NRL grand final breakfast and was written as 'bay marie'. Phonetically close but not how it's spelled.
you can't fight it—it's language change in action, driven here by online gaming. So we can say goodbye to any distinction between alternate and alternative as outlined here. In popular culture at least.
a choice between two (bad) alternatives, so shouldn't really be used to describe a general problem, as in 'When parents go back to work they face the dilemma of working out who's going to look after the baby...' Anyway the sentence is too wordy, and is better as: When parents go back to work they need to decide who's going to look after the baby.
means where two points meet. It doesn't mean on the verge of. Your birthday can be on the cusp of two star signs, but you can't be on the cusp of adulthood.