I may need to change out the battery in a 2004

Batteries die all the time. It is fine to swap batteries. The memory in your cars computer is 'flash' memory and will be just fine after you swap batteries. You will need to reset your clock and if you have a distance to empty readout that 'learns' it might take a few fill ups to get its accuracy back. Your Jeep though will run just fine.

Yes. The computer will store the memory for quite some time actually. It saves information each time the car shuts off. It has it's own backup source. Just your radio will need reprogramming.

To eliminate this worry, you can get a "setting saver" that consists pf a 9v battery and a plug that goes into the cigarette lighter. (found in most parts stores) It keeps the system from going down while doing battery changes etc.

Should be just fine, I try to be sure every thing is turned off, doors closed,etc, so the computers have nothing out of the ordinary to detect.
Make the switch as quick as possible, as some components, such as your stereo may require a start up code if disconnected from a power source too long.(Anti-theft). Clean or replace battery connections as needed while you are at it. Terminal and clamp cleaners are relatively inexpensive.

Hope this is of some help.
Ed