I would like to know if it is possible for org-mode to open its org files in unfolded state, and possibly with specified level (e.g no more than *** headlines) and possibly with option to fold/unfold bodies as well.
You should check the
#+STARTUP directive for per-file default view settings:
You can use
org-customize to set global defaults, or even use the
VISIBILITY property inside a heading to affect a particular sub-tree.
Allowed values include: overview, content, showall, showeverything.
I don't recall an option for specifying a global N levels of visibility (you can put together some elisp for this); anyhow this is quite easy to do on the keyboard (e.g.
M-3 S-TAB will display all headings up to level 3).