หน้าหนา

Yes, in 99% of cases, it is a negative description of someone's character.

Only sarcastically, e.g., 'I'm so shameless for asking for more food.'

'หน้าด้าน' is much stronger and considered vulgar. It's like 'shameless' vs 'brazenly disgusting.'

Use 'ไม่คิดมาก' (doesn't think too much/not sensitive) or 'อดทน' (patient/enduring).

It's an idiom, but it's used very commonly in informal speech, similar to slang.

Absolutely not. It is too informal and insulting.

No, only to people or their behavior.

You could say 'เขาไม่ค่อยเกรงใจ' (He isn't very considerate).

Because the face is where shame is visible (blushing) and where social identity resides.

Yes, especially in rock or pop songs about cheating or bad breakups.