Org-mode - let it open .org files unfolded

You should check the #+STARTUP directive for per-file default view settings:

• http://orgmode.org/manual/In_002dbuffer-settings.html#In_002dbuffer-settings

• http://orgmode.org/manual/Visibility-cycling.html#Visibility-cycling

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).