Help please
#3
Have you done a throttle calibration? Your battery was out, and it probably needs to be reset. Your car is a cable-driven throttle car but it'll still make a difference. Search for "throttle body alignment" for instructions.
#4
My '96 is cable-throttle and has never had idle issues due to the battery being disconnected, although it doesn't have a motor-throttle idle control like the '98. But we also have a '99 Passat 1.8T with the motorized throttle, and also never any particular battery-change issues that I can remember. My guess it that an adaption isn't going to fix rough running. Something else is wrong, and a code scan is where to start.