Right. The concept of ritual purity does not translate well to the modern understanding.
It's a catch-22 of sorts. If Mary is without sin, then she doesn't need the sin offering. But if she does not make the sin offering, then she has broken the Law, a sin in itself.
Yep!
Yep!
And, as was alluded to, the proper path is found in the Baptism of the Lord. Though Jesus certainly had no need to repent of his sins, he underwent the baptism anyway, to point the way for His followers and to show obedience.
SD