Hi Tsiao, yeah like Steve mentions you need to use Trim to actually cut the surface into multiple separate pieces, and when you use Trim it incorporates a projection into it so you don't need to do the projection as a separate step.

Project just generates a new curve object that is on the surface, you could then use it for other kinds of constructions like as the path for a sweep or whatever.

Inset is kind of more oriented towards surfaces that are bounded by sharp corners - it tries to put a border around the inset area by doing an offset of the neighboring faces and it may have some difficulty on things that are all smooth where the pieces meet up.

Possibly instead of using inset you might want to just use extrude or shell on the small surface fragment after you have trimmed it from the larger piece, see here for an example of that:

http://moi3d.com/forum/index.php?webtag=MOI&msg=3024.4
http://moi3d.com/forum/index.php?webtag=MOI&msg=4010.4
http://moi3d.com/forum/index.php?webtag=MOI&msg=3318.1

Also see here for some other somewhat related techniques for grooves and things like that:
http://moi3d.com/forum/index.php?webtag=MOI&msg=3859.2

- Michael