I was not aware of any implied hierarchy with tags. The order is not important as far as I know, and what you describe as mix-and-match seems ok. There is an idea of inheritance, e.g. sub-headings can inherit tags from higher headings.
Same here.
I am not sure about the org-mode tag.
"-" is an invalid tag character.. the tag can be "org_mode", but not "org-mode". Last time I tried using hyphen, I remember that the tag auto-alignment would stop working (C-u C-c C-q) and also the tag face won't be applied.
@Lawrence:
You can have tag inheritance this way:
* Emacs :emacs:
Emacs stuff
** Lisp :lisp:
Emacs lisp stuff here
*** Org :org_mode:
Emacs + Lisp + Org mode stuff
** Org :org_mode:
Emacs + Org mode stuff (but not lisp)