How can I find more in depth site statistics than this on this site? Or on any SE site for that matter?
I believe you can access some data without 5000 Rep. You'll find out real quick once you go there. Here is the location for the data explorer.
Stack Exchange Data Explorer
I do not believe there are any site analytic available here though. As Zaid said you need 5K Rep to get access to that data. At your rate, you should be there pretty quickly though.
The Questions Per Day statistic is mentioned in Area 51.
Click on the Area 51 link to see the QPD statistic.
You can gain access to Site Analytics once you have 5,000 reputation points.