We have ALWAYS pushed our cars off the line.....it saves on clutches and spinning rear tires- BIG TIME!
Mounting ballast way back there may not be a good idea.... Don't try to use it to streamline..... I and a lot of others will protest you..... and yes..... you can tether your 'chute to it and/or mount your pack to it .... pretty much any way you want.
As far as design ideas.... about 12 to 16 inches (300 to 400mm) behind your car.... We use a straight, heavy wall tube that is mounted into a 3 point (pyramidic shaped) support from the rear crossmember to the frame rails- with a wheel mounted in a "forkshaped" pair of plates. The push plate on the truck is 12" X 36" and rides against the wheel. That way, as the racecar/push car each steers independant of each other and will waver sideways when in contact, the wheel allows the two vehicles to "float" without one or the other transferring steering forces to the opposite vehicle.