so my question of the night is
 

was hirschmann the OEM provider to MB for power antennas and can I raise the mast manually, not caring if it retracts? additionally, does the powered antenna have a signal booster included as the signal has to run the length of the car? I don't care about the thing working up and down, if it stays up fine...but I seem to remember that sending a radio signal from the back to the front of a car requires some kind of amplification....is that right?

Several questions, but at least I can answer the QotN:
1. ja
2. don't know. I think it has a toothed nylon belt that you could strip if the motor won't turn.
3. don't know
4. I don't think an amplifier is necessary for the distance given the mast antenna, but the head unit may be designed to need one.

I've never heard of this, must be an urban myth in your locale. As long as the signal wire is securely fastened at each end, no additional 'amplification' is required. Next time you have the radio out of the dash, but still wired to the harness, try running it with the antenna lead unplugged from the radio, but nearby the input socket. You will still get a signal, albeit a weak one.
The amplifier, or signal booster, you refer to is sometimes used to boost a weak signal reception from the antenna mast, caused by a poor mounting spot for the mast/antenna itself, a too short mast, or more likely, geography in the area interfering with the reception, mostly FM.
If you can get the mast up under its own power, then unplug the antenna while it is still up/radio on, it may go down on its own, which suggests the unit is working as it should. If it won't go up under power, you could manually pull it up, but you do risk damaging the gears and/or toothed nylon lead inside the mast. I don't know what you want to end up with, but these are great antennas and easy to repair. Lots of info on the audio forum here.

An antenna is, by itself, a signal booster. There are no other internal circuits that enhance or inhibit signal reception (other than the LD feature on the Becker that filters local carriers so that far-away stations have better reception, but it's a trade-off).

Depending on your setup (model and year), your antenna cable may only be slightly longer than the length of your trunk, as the Becker control unit (including tuner) resides there. The head is merely a control panel. Otherwise there is little measurable signal line loss for cable lengths under 100 feet, even if your cable has to run the length of your vehicle.