Why use wired trainer?!?!? Wireless is so much easier, and it works just fine with the DX9 as the master to a DX6i.
Yes, it's normal operation for all the things you asked about.
I would set up the DX9 in P-Link Master mode. Then the DX6i is just a default model. You control the FM and panic on your DX9, the student just controls the sticks.
My daughter (19) asked me to teach her to fly. We went out two days - 7 flights the first day, 5 the second. By the end of the first day she was nearly ready to solo, and this was with 36 degrees and a 10-12 MPH crosswind. The second day she had 3 solo flights and two landings on the runway.
Andy