มือแข็ง

It's a moderate insult. It's more of a social critique than a swear word. It's like saying someone has 'no home training.'

No! That would be very rude. It's a term used by seniors to describe juniors, not the other way around.

Yes, it can literally mean stiff hands from cold or illness, but context usually makes the meaning clear.

Rarely. Thais usually have lower expectations for foreigners, but they will be very impressed if you know the term.

The opposite is 'mue on' (มืออ่อน), which means polite and respectful.

You could say 'ผมอาจจะดูมือแข็งไปหน่อย' (I might seem a bit stiff-handed) as a humble way to apologize for being shy.

Mostly, yes. It can also refer to a general lack of greeting (not saying hello), but the 'wai' is the core of it.

Yes, to describe employees who don't show proper respect to senior management.

Always 'wai' people who are clearly older than you or in a higher position of authority.

It's more of an idiom/colloquialism than slang. It's been used for a long time.