1995 Honda Civic The Engine Wouldn't Fire Up, I Took it to

My car gave out at a gas station. Its engine would turn over but not fire up. The gas was low. After adding 3 gallons of gasoline, it still would not start. The dipstick showed there was essentially no oil in the engine. Two quarts of 10-40 were added. It still would not start. It was towed to a mechanic who ran a diagnostic on it and then performed a minor tune up and cleaned the fuel injectors.
The car drove out of the garage but stalled while idling (the engine shuddered when the rpm's dipped). It re-started, and after a little while of driving at no more than 40mph and idling intermittently, the rpm's stopped dipping and the car stopped stalling when idle.
I took the car onto a highway and reached 65mph. It drove well for about 5 miles. I felt the engine begin to bump. This continued until the car stopped recognizing that my foot was on the accelerator and it began to coast. It momentarily picked up on the acceleration a couple times and then lost it and I coasted onto the shoulder. There was a smell but no smoke.
I tried the engine, it turned over but wouldn't start.
I called the mechanic who suggested I leave the car off for 5-10 minutes because it might be overheating.
I checked the coolant container and found it empty.

I had the car towed to a gas station. I decided I would try to add coolant. I haven't yet, and I am not sure that is the (only) cause of the problem. I plan to add coolant to the engine and try turning it on tomorrow, but I am concerned that trying to turn the engine on will only worsen the damage that this event may have caused.

As a side note: the engine never registered as overheated, but the oil light never went on when the engine had no oil either, so I consider most of the indicators to be faulty.
The engine had stalled at idle several days before the engine wouldn't fire up the first time.

1. Is the mechanic negligent for not alerting me that there was no coolant?

2. Will trying to start the car cause further damage?