No real policies regarding that except the general one that on an inpatient medicine service you should only ever be supervised by an IM (or neurology) attending and IM residents (plus fellows as per the service). Assuming you have a medicine-trained attending leading your team (that you present to every day), your hospital policy determines who can supervise you doing procedures. It's perfectly normal for that to be anyone else who is allowed to do the procedure on their own, whether that's another resident or anything else you have listed.
In addition, your program and hospital determine the minimum # to achieve "competency" and be able to do it on your own. Five procedures is used as a general guideline for a minimum number of required procedures from the ABIM, but that general guideline only applies to procedures that are actually required by the ABIM (which last I looked was something like only venipuncture, arterial puncture, and pap smear). My program required anywhere from 3 (for paracentesis) to 10 (for intubation or central line) to be able to do various procedures solo.
