So, 4) says it now starts and does not die. Sounds like one of the sensor was bad.

BUt you also say it does not start on the first try. That kinda makes me suspect the sensor(s) they put in. Most shops will run to Autozone for sensors - in that case, sucks to be you. Your choices are to keep chasing this or put the RIGHT sensors in and see what you have after that.

Aside from that, I'd try this:

Get in car.
Turn key to ON.
Wait for a count of three or four.
Turn key to START.

Does it start on the first try then? If so, I'd say you have slow-to-build fuel pressure (which you can test with a simple fuel pressure test kit that costs under $50).