[cheshired5]

The battery doesn't sound like the greatest so what does the voltage drop to during cranking?
Low system voltage can create multiple problems but I doubt even a bad battery is responsible for all of your problems. It would still need charging or even changing though.

Your model year is also prone to failing DIMs (the instrument cluster) which can be fixed cheaply by a guy in the UK. The DIM is also intertwined with a lot of systems so could be a possible cause.

The earliest wiring diagram I have available is from 2005 which would be a facelift so could potentially lead you astray as a lot of electrical stuff changed in the mid 2000s.