Good questions. For now I'll just pick the first one, and I may come back later for the others.
Are these harsher sentences in part caused by a systemic problem with the judicial system?
Most definitely. The fact that men on average get 63% longer sentences for the same crime (and this is pretty much true across countries and decades) tells us this is a systemic problem.
This relates to the societal view on men as having agency and women as lacking agency.
I think that at least we need to have relevant training of judges and lawyers on this subject.
We care. Because there is a lot of negative messaging about men, and young men especially get distorted ideas because of that. As an educator that's important to me.