The employees of Catco could not have "new three-year contracts" unilaterally thrust upon them; they would have to agree and sign. Additionally, perpetual non-compete clauses are unenforceable.
Lena could not just sell CatCo quickly and silently. Sales of corporations this large would have to be reviewed by the Justice Department. As it was a media outlet, the review would take special scrutiny and would take months of hearings.
Kara's glasses are a logistically impractical place for Brainy to put the motion sensor that materializes and de-materializes her new super suit, since she only wears them as part of her civilian disguise; by inference of how the sensor works, in order to change from Supergirl to just Kara, she would need to redundantly put her glasses on, whip them off, and then put them back on. As a 12th-level intellect, surely Brainy could invent a more pragmatic means of allowing her to change from superhero to civilian. Unless brainy found a way for the suit to materialize her glasses and the action of putting them back on was what De-materialized her suit.