It certainly is possible to address both situations simultaneously.  It does depend on the details but a reduction in the size of the nose can be combined with mid-face/lower eyelid filling.  I would suggest that you not use injectable fat but rather a Tear-Trough implant for the hollowness.  This implant is not subject to the unpredictability of fat survival and does not require a separate surgical site for harvest.  It also is far more likely that your hollowness is skeletal, not soft tissue.  The implant directly addresses skeletal deficiency since it looks and behaves as though it were bone once in position.

Doing the procedures separately could potentially make for more accuracy because of greater ease in deciding how much to do at each location.  But with a surgeon experienced in both procedures, this should only be a minor consideration.

The extra skin will not be a problem.  It will contract over the new nose.