1) I'd like to ask you if, besides being more or less formal, there is an important semantic difference between "however", "nevertheless", and "nonetheless".

2) Is there any difference between "be that as it may" and "however that may be"?


Generally, I personally don't read much semantical difference between them.
Tricky. "However" seems simply contrastive:

1. Burble burble burble. However, blah blah blah.

i.e. you haven't necessarily decided between burble and blah.

But "be that as it may" seems to suggest that while you accept the validity of the burble, you have plumped for blah:

2. Burble burble burble. Be that as it may, blah blah blah.