Call around to a few contractors and ask them directly their cost per square foot. They should be able to give you a number right off the top of their head. Then compare theirs to his. Depending on size and regional cost- $10,700 could actually be a little light.
On the sparse tools- When I did residential, we did about the same thing. Usually 2 guys would tear out the turf, grade the ground a little and set the forms. Truck drops the under bedding and that gets wheeled in. Then the bobcat comes in and tears out the driveway and any heavy excavating (for versa-lock or various other walls). Final check up on forms, elevations, and installations of box drains and what not, then we’d pour concrete. Some guys (or Co.'s) will have a few people on standby or working on another job in the final stage while the forms are getting set, then bring them in for pouring/finishing.
A few things you can check in the contract and on the ground-
Thickness of concrete and depth of the forms- they should be the same. You can’t pour 4" into shallow forms. If you check a few concrete suppliers and the price of the concrete for the volume required is more than the bid- something is wrong.
Pitch- make sure it’s tilted where it should tilt (for drainage and what not) and not tilted if it shouldn’t be- like draining into your house. You can lay a 2x4 across the form and put a long level on top of that to get the gist of its pitch.
Under bedding- the gravel or cinder should be in before they pour, and shouldn’t be heaped up or too deep into the forms. If there’s only 2" from the gravel to the top of the form, its going to be thin. (No, it doesn’t sink in and grab the under bedding, not that much anyways).
Reinforcement wire- That goes in right before the pour. If it’s in the contract, make sure its in the forms.
When they pour and finish, a little douching with water is typical toward the end, but if they’re pouring a super loose slurry it’s screwed up and the aggregate will settle and a thick crust of cement will be on top. Conversely, if it’s coming out of the truck in lumps and people are yelling (they’re always yelling), running like crazy, and float scrubbing like their life depends on it- it’s probably a hot load- Started to cure in the truck. That is a disaster. Pouring and finishing is busy, but shouldn’t be crazy. If they go crazy, something is up. If they scrub it too much, you get a bad finish with magnesium burns permanently imbued to the finish.
The owner of the company I worked for used to come to the customer with a portfolio of work so that they could choose the type of finish(brushed, exposed, pattern swirled, stamped), and a list of satisfied customers for reference. Minus that or a stellar reputation (we had both) I’d be a little hesitant.