A few points.
First of all, ZG Grand Cherokees have quite a high ignition off draw and can flatten a brand new battery in 4 weeks if left idle. It even says so in the owner's handbook. So if your battery is old and tired it won't take long at all to kill it. If you're going to leave it for a while pull the IOD FUSE to stop this happening.
If the battery has been flat you need to charge it properly for 12 -24 hours, A jump start and a run round the block will not do-it'll be dead again the next morning. Once you have a known decent battery, if it still going flat within a few days you should check how much current is being drawn with the vehicle switched off and locked (let it rest for a couple of minutes to allow the computers to shut down properly) The normal draw is 500-700mA. If this is all you have, fit a new battery.
The problems you have been experiencing with the door and instrument cluster are normally due to the driver's door module being spiked by the central locking motor, causing it to freeze and block the CCD bus, disrupting communication between the other modules including the instrument cluster. Unplugging it or disconnecting the battery will reset it and restore normal operation. If your battery is low it may be more likely to happen so that needs sorting first. There is also a kit available from Jeep to stop the spiking happening completely which plugs into the harness between the central locking and the door module.
