Bob,
1) Should I say "one ball, one strike" when giving the count or "one and one"? Is either okay?
Either is okay. I mix it up, depending on the situation.
2) Should I be quieter on my "ball" calls?
No, you were just fine. Don't scream "ball," as others have said, loud enough for the pitcher is fine.
3) Was I working far enough from the catcher?
You were fine.
4) How was the timing?
It did not seem contrived, so it appeared you tracked the ball properly to the glove. Too bad the catcher couldn't catch some of those strikes 
.
5) How was my use of the eyes?
I couldn't see, but the timing seemed genuine, so it was probably good.
I echo what Mr. Umpire said. You don't want to hide the arm behind the catcher and leave the slot arm exposed. Looks dumb. Tucking both arms or just the slot arm looks better, and I have seen many MLB umpires doing it, so there's no shame in it. Just don't ever put the arm behind your back, or you will look like the proverbial speed skater.
It would have been nicer to see you on a field and add one more guy to play the batter, but other than that one thing, it looked pretty good. Of course it is no substitute for the real thing, where we can take into account your other game management skills, but as far as cage work, not bad at all.