The delay in connecting is only with the Z2.
There's always the possibility that that's the best the Z2 can do with this specific phone...
I've also noticed that if you turn the volume just a little too high, the feedback to the caller is unbearable.
Yup. Same here, for all phones I've tried. And it makes sense being a speaker phone and all. It'd be nice if it could cancel input matching the speaker output, but I guess this was too difficult for Pioneer

Is there a way just to turn off the bluetooth module in the Z2?
Nope.
You can either unplug it, or do a Level 3 reset of the Z2, which will delete all paired phones (as well as most of your customized settings). Still, better than a Level 4 reset, which delets your library 
I really haven't been able to find much on any of the technical information on the ND-BT1 from Pioneer.
The entirety of Chapter 9 (10 pages) in the Z2 Operation Manual focuses on the ND-BT1 and using bluetooth phones with the Z2. And if you REALLY want to get technical, The ND-BT1 Service Manual is buried in pages 262-288 of the Z2 Service manual, breaking down the circuit layout and EM field transmissions with an oscilloscope.
I've cropped the ND-BT1 Service Manual section and made it available on my site, as well as the other manuals I've mentioned. Link is in signature.