Informed trader needs to be properly defined. Suppose a person just does some research at individual level (read, OSINT, make their own computer models to do prediction etc), then that's permissible.
But if you're defining an informed trader to already know the answer, then it's problematic. I hope you see that as well. The market should reward some logically deduced conclusion, not power. That's my position.
Also it's not noise, an average trader is not choosing a random number between (0,1). They can do research and their guess can be informed. Hence, the use of word wisdom. By your definition, this is gambling then.
No.
Please look at the name again. It's "prediction" market. So if you have credible information before resolution, it's no longer a prediction.
Also your premise is incorrect. The goal of prediction market isn't that. It's to represent wisdom of crowd. Informed traders who can influence the outcome are no longer using any wisdom, nor they're part of the crowd.