As you found out, pumps can move a lot of water! When I had my sand filter, I ran a pipe to a corner of the yard, that I didn't mind flooding. I had a stub on the discharge point (mine was off of the selector valve) and then used one of those temporary rubber couplings for pipe repair from the hardware store to the long pipe, so I could attach other hoses to the output, if needed, to send it other places. Note that some localities have rules about discharging on the ground, or into a storm sewer. Mine doesn't.
For the pump, when you turned it off, with the waste valve open, air got sucked back in as some of the water drained back to the pool. Happens all the time. You "lost prime". Have the pool guy show you how to recover, as each setup may be a little different. No harm, as long as you don't run the pump for long periods without water in the system.
At this point, just leave it off until daylight. You can then at least get the rocks out of all the baskets.
Can't guess as to how detrimental wet fine cement will be to the system. Might begin to set and glue the sand in the filter together (might be "chunky" but not a solid block of cement), might stay fine enough to not be an issue. Have your pool guy evaluate. Sand is replaceable, and not a big expense, if it comes to that. Cement may settle and harden in other places (pipes, heater core, on the pool itself, etc.), that the pool guy should evaluate. Pretty impossible for you do to anything to flush it all out on your own, especially with an incomplete setup. You did much more than many would/could do.
Since this doesn't sound like a DIY project, the installers and concrete guy should have insurance to cover the mistake. Insurance should pay to replace a lot of the equipment if it comes to that, especially if your pool guy has any doubts about how "like new" it will be anymore. Hard to forecast at this point how good/bad the situation is. Stick to your guns and demand that they get it back to 100% "like it was". You've done what you can to help them out, but they are supposed to be the "pros". Hope they are an upstanding company, and you don't have to go legal on them!