Yes, antenna amplifier power is provided from the head unit through pin 9 of the 20-pin connector (one of two) on the head unit. Whether or not that is still applicable would depend on the new head unit, and if the connection to the car’s wiring was ‘”plug and play” or had to be “adapted”.
Does “other stations interfere” refer to listening to AM, FM or both?
The antenna traces on the rear window can develop cracks, or be damaged when cleaning the rear window or if objects are touching it. A close inspection of the traces (perhaps with a magnifier) might reveal this is the case. Broken traces can lead to poor reception.