I hired a plumber to set my bathtub and put in the trap for the drain. He jackhammer the concrete to get a trap in.

Question #1. Does the hole in my concrete need to be sealed with cement? He just put rock back into it, but no concrete.

Question #2. Is it possible now to shift the tub about 1" backward once the drain is already hooked up, or will it mess up the pipe fit.

Question #3. In relation to question 2, I framed the walls so that there was 1/2" on all 3 sides of the tub between the framing so that I could fit drywall in between. This is the reason for question 2, because he pushed the tub all the way to the front wall and now I have about an 1 1/2" gap in the back. I don't know how I will fill the gap without moving it.

You errored in leaving 1/2" for drywall. The tub fits up against the studs and the drywall overlaps the lip of the tub. You can re-pipe the drain and move the tub or you can fill in the wall with additional framing material. Why 1 1/2" if you left only 1/2" on each end of the tub, should have a 1" gap. If you have 1 1/2" add a 2x3 to the edge of each stud and make the wall fit the tub. If toilet is on that wall, plan on using an off set toilet flange.

I hired a plumber to set my bathtub and put in the trap for the drain. He jackhammer the concrete to get a trap in.

Question #1. Does the hole in my concrete need to be sealed with cement? He just put rock back into it, but no concrete.

Question #2. Is it possible now to shift the tub about 1" backward once the drain is already hooked up, or will it mess up the pipe fit.

Question #3. In relation to question 2, I framed the walls so that there was 1/2" on all 3 sides of the tub between the framing so that I could fit drywall in between. This is the reason for question 2, because he pushed the tub all the way to the front wall and now I have about an 1 1/2" gap in the back. I don't know how I will fill the gap without moving it.
Meh, I typed that wrong. It is a 1 inch gap. So that answers questions 2 & 3. I'll just find a way to fill the gap now.

Still need an answer to first question. Do I need to remove the tub and pore in some concrete, or just leave it rock?

Question #1. Does the hole in my concrete need to be sealed with cement? He just put rock back into it, but no concrete.
The tub dap-out should be left open and a access panel installed behind it.
This is so the tub waste and trap can be serviced if necessary. Good luck, Tom