Three grand?!? I think I would remind this mechanic that his fees are for competent diagnostics performed to industry standard as well as just randomly replacing parts, a fact that often stands in small claims court...

Stop swapping parts and start measuring. Put in a new set of copper plugs gapped to spec (Bosch or NGK) so that it will run while you diagnose.

Pull the OBD codes as others have suggested. There may be meaningful clues there. More often than not they provide clues rather than "smoking guns" in my experience...

Measure fuel pressure at the rail. Pull the vacuum line at the front of the regulator and smell/look for fuel. I know the part is new, but not all new parts are good. See if you have fuel bypassing out to the return line (back of regulator). You have rich running symptoms (gassy, missing, hard start, black exhaust) that point to FPR, ECT sensor stuff.

Get a noid light and see if you get consistent flashes at the injector harnesses. If you do, it is much less likely that need a new ECU. If the injector function is flaky you may have a problem with the power stage, although the classic failure mode is poor running/stalling/no-start when hot.

Check spark on all 4 cylinders-- you can use a spark plug or a spark tester. If you get consistent bright spark your ignition system is OK (as is your RPM sensor). Inconsistent spark could be the RPM sensor, or the wires. If you need wires, buy Bougicord.

Measure the output of your new coolant temp sensor at the ECU as per the 700/900FAQ. Did the mechanic replace the forward sensor (gauge) or the one between runners 3&4 on the intake that actually talks to the computer? Bad connections or a bad part here could cause the car to run really rich and foul the plugs in short order. Bad contacts in the ECT harness plugs are reported here from time to time.

Pull the timing belt cover and verify the engine timing as per the 700/900FAQ.

Bypass the fuel system relay and see if the car runs better-- search the archive for lucid's method of jumpering fuse 4 & 6. Or replace the relay to see if the running improves.

If the car has been running rich for a long time the cat may well be toast. FCPgroton.com has them for about $130-- I had to put one on my '92 245 before I sold it-- it was a Canadian made Davico and it seemed like a good part. If you have been smelling a "rotten egg" smell, it is quite likely the cat is cooked. Just replacing it isn't going to fix anything, though-- you need to find out what made the car run rich and kill it or you will need one again by the next emissions test.

Measure the output of the sensor line on your 02 sensor with a volt/ohm meter. I'll bet it is pegged on the rich side rather than fluctuating between .15 and .85VDC. I had a new Bosch sensor that was putting out 1.4V, which made the car run just terribly. Some have suggested that this can be caused by stray voltage from the heater circuit.

Have a close look at the connector wiring for the AMM. Did you get a new or a rebuilt AMM? Which LH system does your car have? It is either LH2.4 or LH3.1, and this will determine what AMM you need. Does the car idle better with the AMM unplugged?

The advice on setting up the throttle body is good too. Make sure the idle air motor and the throttle position switch harnesses weren't swapped.

Check for vacuum leaks at the intake manifold, look for holes in the intake snorkel and check all the vacuum lines.

Check which ECU you have-- if it is a pink label -561 (the last 3 digits of the part number), it is a known problem ECU. White label -561 or a -951 are better. The ignition computers (ICU) seem quite robust. The ECU usual failure is no grounding of the injectors, so no noid light flashing, so don't go buy one without checking injector function unless you have access to a used one cheap that you can prove is good.

I am sorry to hear about your troubles-- report back on your measurements and you will get help from a lot of smart people here. I am continually amazed at how helpful brickboarders are!

Good luck!