Yes, which led to the replacement of people with good intentions to people like Norman Osborn. Things are going to be worse, not better.
They were always going to get worse. AFAIK Osborne already controls everything to do with the Initiative, this doesn't imapct on that one way or the other, excpet highlighting to the population the corruption in the system they so embraced.
If anything, that's just an argument for why he should kill the Joker.
No, it's really not, because that's not Batman's mission statement and never has been. If the Police and Arkham can't contain the Joker, despite the funding he supplies as Bruce Wayne, that's not HIS problem per se.
However, Batman not stopping an immediate threat is not comparable to Justice keeping quiet about something that if revealed would only lead to more problems.
"more problems" which were already there and waiting to pounce.
And things will be better for her now that Norman's in charge?
Who knows, he shut the camp didn't he? Have we seen what's happening to the inmates?