If the inside shape is correct and the rebar is about in the middle of the gunite, and it's thick enough, what the back looks like doesn't really matter. There shouldn't be any organic material behind the gunite if there is going to be backfill and a deck poured, because the organic material will rot and leave a void. The forms should all be cleared out for that reason, but a few scraps would not make a huge difference. If there is too much of it, or even if you don't like it, then ask the PB to have it all removed.
The little piece of rebar looks like it ends on the right. If that's the case then it can't be doing much in the way of structure or support. His explanation of how they'll cut it off and mortar it over is what I also thought would be an OK fix. It's not clear why it's there, perhaps it's as you guessed, just to hold the skimmer at the correct height. You just need to follow up and watch the sub do that, as sometimes when a detail gets passed along it can get overlooked.
I think it's good to stay on top of these things. You just have to temper it to make sure you're not overstepping or second guessing your PB more than necessary. Asking about issues here is a great way to keep both the builder and you in check. So keep the questions coming.
So far, I don't see anything too weird about the work, or too weird about you asking about it. It sounds like you've got good communication between yourself and the builder, and that's the ideal situation.
@jimmythegreek, do you see anything of concern so far?