| | Re: so vs very
I was teaching this lesson just the other day. It seems to me that 'so' often (not always) has a connotation of surprise - ie, sth is, or occurs, to a degree that is greater than expected. It can also indicate an ellipsis (leaving words out), and imply a result that is not said, but can be imagined by both speaker and listener: "There were so many people there! [... that I could never count them all.'] 'I was so embarrassed! [... that I wanted to die.'] The left-out information could simply be "The movie was so good! [...that I was surprised, because I thought it would be ordinary.']
As for your questions above:
1: 'Really' should be hotter than 'very.' "Really" should be said with more emotion than "very" and so it certainly seems hotter.
2. 'Incredibly' and 'extremely' are pretty much the same. (Think of the literal meanings: the first is 'unbelievably' and the second is 'to an extreme, ie, as hot as possible.) Both are probably exaggerations for effect.
3. The 'so' in here is NOT surprise, but indicating 'to the extent that I can see.' ("Why are you so nervous [... that you are pacing back and forth?"]
4. A: The meaning is a strong 'very.'
B: The repetition of "You were so nervous?" sounds odd. "Why were you so nervous?" is asking about being nervous to that extent - the extent that A implied by her comment.
6. T's reply is not very natural, unless the 'so' is stressed very strongly ("I'm soooo busy!") If not, it sounds like an non-native speaker's mistake. Of course it can be understood, but it's not what we'd say. 'Really' or 'very' would be more natural.
J's response, however, is fine: "Why are you so busy [to the extent that you're not free]?" I think it's not showing surprise at being busy, but the extent is unexpected.
7. A's question is not natural English. ("Is she very weak?" "Yes, she's so weak that she can't raise her arms" would be OK.) Maybe 'Is she so weak?' doesn't work because it's a question, and so the speaker can't emphasise the extent of the weakness because they don't know it yet.