No, iPad Air does not fit with Perch's holder.
Please pull the neck lock up as far as you can and use a thin but sturdy object to poke through the small cutout and push the button to take off the holder.
The neck lock is not designed to be zero tolerance snug fit. It is completely normal that there is still a tiny room of maneuverability after neck lock is correctly installed.
Yes, it is. The lock can be easily installed and removed at 360 degrees. Being able to spin the lock is perfectly normal and does not mean your iPad is not securely locked.