One question per day, please.
First of all, I'm not sure what "womanly sins" are, or how they are different from "manly sins." Second, a sin depends on the context of the religion and the personal relationship with God. So, Hamlet would not be in a position to judge Ophelia regardless; her sins are between her and God.
Having said that, I don't think she commits any obvious Christian sins. In the very Christian play Hamlet, Ophelia is rather blameless. The only mistake she makes is being a pawn of her father directly and king indirectly. She gets caught in the crossfire of male versus male revenge and suffers dearly for it. Her role is a sub-eiron: one who suffers by extension. She is no doubt a victim of male sexism.
But, here's the rub. I don't think Hamlet is talking to Ophelia at all when he says "get thee to a nunnery." Hamlet is talking to his mother. Hamlet knows that Ophelia will relay his words to her father, and her father will relay them back to Claudius, and Claudius will relay them to Gertrude. Hamlet is judging Gertrude, not Ophelia, with this game of telephone. Hamlet wants Gertrude to feel guilty and confess her crimes of incest and hasty, illegitimate marriage.
Second, Ophelia is a sacrificial lamb in Hamlet's revenge plot. She's the "whipping boy" who must hear his painful words. Hamlet is the hero in the main plot and all the subplots except this one: with Ophelia Hamlet is the villain. He knows this, but his duty to his father as an avenger supersedes his duty to his girlfriend. Sadly, Ophelia is Hamlet's pawn too.