AUM: Asset under Management refers to how much money a hedge fund or financial institution is managing for their clients.
Adjusted close: Same as actual close for today. But as you start going back in time, the values diverge since the adjusted close accounts for stock splits and dividents paid and constructs a uniform view of closing price normalizing for splits and dividents.
Doing historical analysis by considering stocks that exist today. This leads you to avoid performance of stocks that have entirely died out in the past creating a biased outlook of the market by considering only the ones that survived harsh market conditions.