When was Moses circumcised, and by whom? — S.W.
First, let’s read the passage about Moses’ birth. We read in Exodus 2:1-2, “Now a man from the house of Levi went and took as his wife a Levite woman. The woman conceived and bore a son, and when she saw that he was a fine child, she hid him three months.”
Circumcision for the males among God’s people goes all the way back to the time of Abraham (Gen 17:10). It was mandated for the eighth day (Gen 17:12). As Moses’ parents were of the tribe of Levi, it is reasonable to assume that they conscientiously observed the circumcision law. They may have circumcised their son themselves, or had someone else do it. When Abraham received the command, he immediately obeyed. He was circumcised, as were his son Ishmael and all the other males living in his household. There is no reason to doubt that Amram and Jochebed followed the law (even if it was not yet “the Law of Moses”), and had their son circumcised on the eighth day.
In both cases—that of Moses and that of Abraham—we aren't told who circumcised these men. Yet the procedure is simple (even if not painless), and there should have been no logistical issue. Flint knives were common, safe, and hygienic, so presumably these were the tools used for this minor surgery. (See Exod 4:25; Jos 5:2-3).
So, to answer your two questions: On the eighth day, and we don’t know.