Has Muzan ever been a human before?
A millennium ago, during the Heian Era, Muzan was turned into a demon during an experimental treatment trying to cure his terminal illness and his goal since then was to live without the fear of death and become truly eternal.
Why is Muzan impersonating a human?
Muzan is impersonating humans and blend in with human society to create networks for information gathering and to secure funding using the different identities he assumed, without the humans he commands and manipulates being aware he is a demon at all. He don't want to be in the demon form roaming in the streets and while in human form, he can keep his identity a secret.
When Muzan was disguised as a child in Season 2, why weren't their parents suspicious when Muzan disappeared for a few days?
In the latest cover identity, he became a sickly son to an old couple. Muzan has the ability to manipulate and erase human memories. So, he altered the memories of the parents into thinking that they had a son. Once his work is done, he can erase the memories. Even if they become suspicious, he can erase their memories or manipulate them to commit suicide (just like he did with his previous five wives) to avoid suspicion of killing. But I believe he can only move outside in the nights and he always keep his door locked, so I don't think the parents are aware of his whereabouts (they know he can't go outside without parents help).