몸이 풀리다.

Yes, but '스트레스가 풀리다' or '긴장이 풀리다' is more specific. '몸이 풀리다' implies the stress was making your body stiff.

Yes, if you want to describe how you've become more comfortable during the conversation. '이제 긴장이 좀 풀리고 몸이 풀리는 것 같습니다.'

'풀리다' is an idiom/native word; '해소되다' ({解消--}) is a formal Hanja word. Use '풀리다' in speech.

Yes, but be careful! '다리가 풀리다' often means your legs gave out from fear or exhaustion, not necessarily relaxation.

Use the active form: '몸 좀 풀어야겠어요.'

Yes, it's the exact equivalent of getting your muscles ready for a game.

Yes! '날씨가 풀리다' means the cold weather is getting warmer.

It is neutral. You can use it with anyone as long as you use the correct politeness ending (e.g., -어요).

It is the most common phrase to use after a massage.

'몸이 굳다' (body hardens/stiffens) or '몸이 뻣뻣하다' (body is stiff).

Constantly, especially in medical, sports, or office-themed dramas.

Usually, we say '속이 풀리다' (the stomach/insides are unraveled) for hangovers.