Hey James, these are excellent questions, and relevant to my own experience because I have the same car and I haven't driven it in weeks. I'm worried about flat spots on the tires too!

Seriously, it's much better to drive your car occasionally if at all possible. There are all sorts of issues (lubrication, hoses, fluids, etc) that come up if it's left to rot. About the battery charging, here's what the manual says:

"Never charge a battery while still installed in
the vehicle unless the accessory battery
charge unit approved by Mercedes-Benz is
being used. Gases may escape during charging
and cause explosions that may result in
paint damage, corrosion or personal injury.
An accessory battery charge unit specially
adapted for Mercedes-Benz vehicles and
tested and approved by Mercedes-Benz is
available, permitting the charging of the battery
in its installed position. Contact an authorized
Mercedes-Benz Center for information and
availability. Charge battery in accordance with
the separate instructions for the accessory
battery charger."

 

Incidentally, the jump start procedure involves the main battery in the trunk. I used it once to help start a friend's SAAB which had died. Meanwhile, I would definitely NOT try charging the battery at all without consulting my service advisor at the dealership. Would you let us know what he says? Otherwise I may ask mine, as I've been thinking about hooking up a trickle charger to my E350.