Is it permissible to perform Umrah if the circumambulator is unable to precisely determine the location of the Black Stone due to overcrowding? And is it valid for the one in a state of Ihram to cut the hair of the performer of Umrah after Umrah without him (the one in Ihram) having performed Umrah himself?

The circumambulation (Tawaf) must be completed with seven circuits from the Black Stone to the Black Stone. The Tawaf is not valid if anything is missing from it, even a single step. It is not required to stand on the line when starting or ending the Tawaf; rather, it is sufficient to be parallel to the Black Stone. If you exerted effort in determining the location of the Stone and performed seven circuits, aligning with it based on your strong presumption, then your Tawaf is valid. As for cutting the hair after the Tawaf and Sa'i, there is no objection to it, and it is permissible for anyone to do it, whether they are in a state of Ihram or not.