How does replacing the battery effect the pcm

How about the water pump ? Who replaced the parts ? A qualified repair shop ? Were codes checked ?
The PCM controls the electro-viscous fan clutch engagement. The PCM regulates a 12-volt pulse width modulated signal (PWM) to the cooling fan relay. The PWM signal determines the ON time of the relay. As the commanded state of the fan clutch increases, so does the ON time of the relay. This ON time directly effects the amount of time the solenoid, which is internal to the fan clutch, is energized. When the solenoid in the fan clutch is energized, it opens the spring loaded valve and allows fluid to flow from the storage chamber to the fluid coupling of the cooling fan clutch, increasing the fan speed. When the solenoid is de-energized, the spring loaded valve closes, and blocks the path of the fluid to the fluid coupling of the fan clutch, reducing fan speed.
The fan has the ability to create a feedback signal, so the PCM has an actual fan speed input. This is done with a hall effect sensor internal to the fan clutch. The PCM supplies a 5-volt reference and a low reference to the hall effect sensor. The hall effect sensor returns a signal pulse through the cooling fan speed signal circuit in response to the relucktor track passing by the magnetic field of the hall effect sensor.
Was electrical tested before fan clutch was replaced !

No ,the box is probably not bad , but you need to have it programmed . The dealer is the only one that can do that ? The keys don't matter .
The passlock sensor mounted to the ignition switch assembly is located inside the upper right side of the steering column. The passlock sensor contains two hall effect sensors: a tamper hall effect sensor and a security hall effect sensor. The tamper hall effect sensor is mounted on top of the security hall effect sensor. Should someone attempt to defeat the system by use of magnetic experimentation, the tamper hall effect sensor will activate first.
The passlock system is a vehicle theft deterrent system which deters drive-away vehicle theft by disabling engine operation if the ignition lock cylinder is not rotated with the proper mechanically cut key.
The passlock system is made up of an ignition switch assembly, passlock sensor, body control module (BCM), instrument panel cluster (IPC), and a powertrain control module (PCM).
The ignition switch contains a magnet mounted on the lock cylinder and a passlock sensor assembly which consists of security hall effect sensor, tamper hall effect sensor, and output resistors. A drill proof metal shield is also staked over the sensor housing.
The passlock sensor mounted to the ignition switch assembly is located inside the upper right side of the steering column. The passlock sensor contains two hall effect sensors: a tamper hall effect sensor and a security hall effect sensor. The tamper hall effect sensor is mounted on top of the security hall effect sensor. Should someone attempt to defeat the system by use of magnetic experimentation, the tamper hall effect sensor will activate first.
The BCM has the passlock controller integrated into it which controls the majority of the security systems logic. The BCM reads the data from the passlock sensor continuously. If the data is correct and has been received by the BCM within a specified time, the BCM will send a coded password to the PCM. The PCM will then allow the fuel injectors to operate.
The coded password for the security system is sent from the body control module to the PCM via the class 2 data link. If the password is correct and received within the specified time, the PCM will allow the fuel injectors to operate.
Sorry but you can't just replace parts , you need to know how the system works . You need to take this to a ASE certified repair facility that knows how it works .

did the original pcm have thee missing pin, they may not be missing they may be left out in engineering, as far as the trans not shifting, was the pcm reprogramed because if you just installed out of a box it unlikly that it will shift

The battery was disconnected or you may have a bad ground. The good thing that it should not effect the operation of the car. It basically lost stored data and it must get it again. However, something is preventing it which means a bad ground, PCM was replaced/bad connection, quick learn for PCM. Other than this, you need a tech who will be able to test the PCM (they need a tool to test so the connnectors are not damaged) with a test light, Fused B+ circuits and/or ground circuits. However, before doing all that, bring to an auto parts store and get them to turn the light off. That may resolve it since this is not a "problem" code.

you can replace battery with out effects.first turn off radio.before removing negative battery cable.when you install new battery, when you start the engine let it idle until get operating temperature.the computer will have to relearn it memory while engine idling operating temperature.open throttle a little see if engine hesitate. it will hesitate some, when you can accelerate with out hesitation,engine tps sensor has relearned it position.if idle speed stable engine dont run rough and stall out in drive your pcm has relearned itself where you can drive it.

the plug on the alt will some times go bad usually melting this is normally the cause of this

Always disconnect the battery before replacing any computer parts.
And yes mileage should get better.

Your generator is pcm controlled. So is the charge indicator. Any charging system trouble codes? The gencom circuit is signal from pcm to generator. The genmon signal is from generator to pcm. Even at idle if you turn on a load, there should be a reaction, engine speed may increase as well as generator output. By load,I'm talking about headlamps or hvac something. At the moment I can't rule out your generator? I hate to see you replace anything and it not fix it?

Reset what the PCM?

If you are talking about the PCM you can have the codes clearded for free at autozone, or you can disconnect the battery for 5 minutes and this will clear any current codes, however thiere will still be old codes stored in keep alive memory but they will not effect engine management.

pulse count modulator, there is a half circle of steel in the distributor, when the steel half circle passes a hall effect sensor ( pcm ) it tells the engine to fire on cylender number one. and the other half of the steel circle exits the hall effect sensor it tells it how fast it was turning. so all the other spark plugs fire at the correct time. The other part is that the pcm cystem is part of a coil that is wound around plates of steel if the plates of steel get wet (over time they tend to rust ) the rust swells the steel and the coil gets broken by the expanding rusty steel. so replace the coil portion of the distributor. just follow the singel wire to the block of steel ( coil is encased in rubber or molded plastic. ) but the coil is breaking or getting stretched and bearly touching and when it gets hot the metal expands too. and it fails. just follow the singel wire inside thedistributor to its coil : replace that and your good to go.