Help 2001 Dakota

1st thought would be the pressure transducer is bad.
Used to replace those quite a bit back in the day.
What is happening is the pressure transducer is sending a signal to the PCM that the pressure is either to high or to low, the PCM in turn is disengaging the clutch by way of the hi/lo pressure switch. the P/N is 5072138AA and they're not cheap. As I recall, you may also have to buy a wiring harness also. They changed the connector from round to square or vice/versa. That should resolve your issue.
As for problem #2 without a meter, I'm guessing, but I'd say you have a draw.
1st thing I'd do is clean the battery top with baking soda, get all the dirt off the battery. After that, it's a game of follow the current.