[AKCJ]

A few ideas:

1. If the car doesn't crank very well you may just have a low or weak battery or bad connections.
2. A common problem is the speed and reference sensors or the connections to them. Do a search - there is tons of info on them. These are what your mechanic was referring to.
3. The DME relay is almost always suspect as mentioned above. Get one and change it out just in case that is the problem. If not, then you needed a spare anyway.
4. This doesn't seem like an AFM problem to me but it wouldn't hurt to read up on it.
5. It's possible there is a fuel problem. Best to confirm that you have fuel pressure at the fuel rail but at least confirm that the fuel pump starts when you try to start.
6. Wouldn't hurt to look at the ignition system. Spark plugs, wires, cap, rotor, coil.

Good Luck