The "sketchbook" concept may not be explained very well....
It's a folder where all your work goes. It's meant for only the files you've written.
If you have many copies of Arduino on your computer, they all are supposed to read files from the sketchbook folder, and default saving files there. So the files you create are meant to be in the sketchbook folder.
A copy of the Arduino IDE is NEVER meant to be in the sketchbook folder. Normally, you should not need to chance the location of the sketchbook folder. It's meant to be your ongoing collection of stuff you've created. When you run Arduino 1.5.x or 1.6.0 or even the old 1.0.x copies, the File > Sketchbook menu is the stuff you've written. All copies of Arduino look there for your stuff.
They also allow you to put extra libraries and hardware files there.
This is the huge problem. In designing the ability to override stuff in the IDE by placing things into your sketchbook, it seem the Arduino devs didn't consider what would happen if you mistakenly set the sketchbook folder to a copy of the IDE. You're not ever supposed to do that. It's probably something noone has really considered.
But from all these weird problems, and the info in those logs, clearly what's going wrong here is you're setting the sketchbook folder to the location of a copy of the Arduino software. The software doesn't know how to deal with that. It doesn't, but really should disallow such a setting, or refuse to startup and give you a helpful error explaining why it can't run. But nobody's ever really considering this situation and understood the issue (or if they have, I'm not aware of it).
I filed this as a bug on Arduino's issue tracker.
https://github.com/arduino/Arduino/issues/2719
Eventually, the IDE really needs to be updated to prevent this misconfiguration and also detect it if it does somehow happen.
For now, you can recover by just making an empty folder, and use File > Preferences to set that to be your sketchbook. If you have files you've written, just copy their folders into the empty sketchbook folder.
Whatever you do, never select the location of a copy of the software with File > Preferences, and never extract a copy of the Arduino zip file into your sketchbook folder.
Once you get a clean sketchbook folder, I'm sure all these troubles will be solved.