Engine died while at a stoplight

Two days ago, my 2004 manual Passat wagon died whilst sitting at a traffic light. Note, I'm in Miami, FL, so it's incredibly hot outside, which seems to worsen the issue. Numerous attempts at turning the car on resulted in cranking, but the engine wouldn't actually turn on, though the battery worked perfectly fine. An hour later, however, when the tow truck arrived, the car started perfectly. I had it towed to a mechanic out of precaution, regardless, but they weren't able to begin working on it until this morning. Apparently, when they went to work on it, it started perfectly fine as well. When they ran a diagnostic test on the engine, these were the codes that came up: p0322, p0300, p0301, and p1237.

They wanted about $200 for the sensor indicated by the first code, and they wanted about $1,000 to fix the ignition misfire indicated by the latter three codes. I went and retrieved the car from the mechanic today (I was not about to blow over a grand on the ignition misfire. It started fine again, and ran well enough to get me home, though the check engine light came on. They charged me about $100 for the engine diagnostic test, but they said they'd deduct that from whatever cost they'd charge me if I went back for a repair. (Which is hopefully somewhat reassuring, though that $1,000 is still asinine.)

Any information about the codes and about the sensor, as well as whether I should go get it replaced would be greatly appreciated. Thank you so much!