Hi ndrakey,

re:
> Is there a way to convert face selection to selection of boundary edges or points of
> that face and vice versa?

There isn't any way to do the points one, but for edges a script like this might be what you're looking for:
http://moi3d.com/forum/index.php?webtag=MOI&msg=5922.37

or maybe this:
http://kyticka.webzdarma.cz/3d/moi/#SwitchSelectionFromFaceToEdges

Set up those scripts on a shortcut key (Options > Shortcut keys) to use them.

- Michael