I need to replace the battery. Can the battery be disconnected without causing reset problems with the car's computer systems, radio, etc? Or, is it advisable to maintain voltage across the terminals using a smaller 12V battery?

 

I like keeping a history of my MPG in the 'trip' computer setting and lost that when I changed mine.
You might also have to re-learn the windows & sunroof up/down by fully opening / closing them and holding the button an extra 2 seconds.

 

No worries, just change the battery, Nothing will get messed up. BTDT.