Keep it in the 'very cold' setting if your planning trips of 30 miles or so. I find that switching to just 'cold' is better if you know your going to be travelling 40 or 50 miles, you end up using engine heat to keep the cabin warm, instead of your stored electrical traction energy.
Yes, this is advised. It will help keep your battery warm and ready for a trip. (and cool in the summer)
I live in Detroit. My bill for the month was ~$50. I think the remote starts and shorter range of the car leads to higher consumption. I used 300-400 kWh to charge my car over 35 days