Number two cylinder misfire

P1586 Encoding Signal Not Rational - MT/AT Encoding. IE the ECU doesn't know if you have a manual transmission or an automatic. I'm thinking you have a "parts" car. They took various bits from one car and tossed them onto this one to make a runner. Very possible that engine and ECM came from a manual transmission vehicle and now it doesn't know it's running an automatic. Look at the wiring diagram attached and you will see the "drive position switch" connection. Check the two fuses listed (9 and 10) and see if either is blown. Then look at pin 86 on the ECU. Should be a White wire with black stripe. On an automatic that wire should have battery voltage when the transmission is in park or neutral. The rest of the time it should get nothing. That could be the cause of the idle and lurching as the ECU doesn't know what to do.

Should be in the fuse panel in the dash.

Different wire. The white with black you need should be from the transmission park neutral switch up to the ECM, it feeds battery voltage from fuse 9 to the TR switch which then tells the TCM which gear you are in for starting and then goes up to the ECM and through a diode set and that tells the ECM if you are in park or neutral. For the rest of the gears it sends no voltage to the ECM. The signal to the ECM is on pin 86, To test it the easy way you can use a test light connected to ground and stick a pin through the insulation on the wire that you can seal with a dab of glue or liquid tape. With the key in the on position that wire should have battery voltage when the transmission is in Park or Neutral. In all other gears the light should stay off. If it doesn't come on at all you have a broken or disconnected wire, if it stays on in all gears it is shorted somewhere to power. Use the meter and see what voltage it is at.

It should be 3 pins in on the end in position 86. If it's not there then that is the problem and it will need to be fixed to cure that code and likely make it run better as well. That wire should be there on both the manual and the automatic cars. Could you take a picture of that connector up close on each end and post it please? The diode Z02 that feeds the wire should be in or near the EM02 connector circled in the image, it will have Black wire w red stripe and a Blue wire with white stripe in one side and the White wire with black stripe out the other. If that is there it would be possible to run a wire or trace the wire that comes out and see where it goes.

The ECU for your car should have a large single connector for the wiring harness. The part number should be 39150-23956 or 39150-23951 as in the first image depends on the emission package. It is inside the car up under the dash.
The unit you are showing is the Transmission Control Unit. By the part number it is the correct unit for a 2000 at least.

That is due to the engine switching to a default programming with the MAF unplugged. However it's possible the MAF does have a problem, they can skew a bit and still not set a code. Normally they will set a P0102 or P0103 if they are out of range.
This is the testing for the MAF-

1. If the engine stalls occasionally, start the engine and shake the MAF sensor harness. If the engine stalls, check for poor contact at the MAF sensor connector.
2. If the MAF sensor output voltage is other than 0 when the ignition switch is turned on (do not start the engine). Check for the faulty MAF sensor or ECM.
3. If the engine can be idle even if the MAF sensor output voltage is out of specification, check for the following conditions:
Disturbed air flow in the MAF sensor, disconnected air duct, and clogged air cleaner filter.
Poor combustion in the cylinder, faulty ignition plug, ignition coil, injector, and incorrect comparison.
4. Though no MAF sensor malfunction occurs, check the mounting direction of MAF sensor.