"email" is French for "enamel." Use "e-mail."

"Let's be friends" is a quite proper shortening of "Let's you and I be friends."

The Chicago Manual of Style, while quirky in spots, is the resource my typesetting company has used for many years. Understand that some rules are disputed and some situations have more than one OK solution.

You're right to catch this. Contrast:

Man/lady man's/lady's

Men/ladies men's/ladies'

that help?

Contrast:

Are we there already?

Are the kids all ready?

The cat's doing what's called "milk treading." Kittens do it when settling down against mama cat for a feed; it stimulates milk letdown. Cats generalize kitten behavior to their people (you are mama cat), so it's affectionate.