Consider the phrase "power has purpose".
I think given the level that Mother Winter exists on i.e. there is only one Mother Winter in all the multiverse, and she ranks around the same level as Archangels and Greater Gods (to use the old D&D scale), I would say that much of what she does is at an environmental level. For example, the fact that entropy and fear and savagery exist in all these many universes. She is powering all of that. Or perhaps not simply powering, but a result of that. If you really think about it, what she is "doing" is constantly shown. Harry just isn't looking that deeply. She is the "Unmaker" after all.
I bet she has chosen a Knight, although I don't believe Jim has ever hinted at it. But probably the most savage and psychotic Winter Knights were probably hers.
To number three, I think the answer is more complicated. The whole bit in Cold Days where she and Mother Summer argue about who's weapon Harry is, and who's world it is etc. Yes, I think Harry is her weapon in that he is an agent of destruction. Whether she was more directly involved in the Star Born part is harder to know - although given that a large part of her purpose is to fight Outsiders (or provide the multiverse with the power to do so, in the form of the many Winter Courts) - I would say it's highly likely.
