I've got the pioneer avic f80dab and it has the same problem. A real pain in the butt for the reverse camera.
Sometimes it's instant, sometimes it's a minute. No pattern
I have the OEM Audio Plus and music from my iPhone 6s is great through both Bluetooth and direct connect.
The stock speakers for the BRZ were soooo bad. I couldn't listen to music through them. It was a horrible experience.