Water won't turn on due to cold weather suggestions?

not likely to help.
Your pipe might be frozen outside. (not deep enough)
Heating your house will not help with that...

Cranking the heat up won't help. As stated, once the pipes thaw there will likely be water squirting out of a section of the pipes which have been burst by the ice. The next time it gets cold, leave a faucet or two trickling. Moving water tends to not freeze. You should also look into getting heat wrap put on the pipes or at least insulate them.

Your no water situation could also be a problem with the pump - idf there even is a pump. You provide so few details that it is difficult to give a very good answer.

Probably not. It's hard to say for certain without knowing just how your house is plumbed. It's likely that you'll have a leak once it warms up again, as the ice in the pipe will have burst it.

I think a lot of people will leave a drip or a little trickle of water on overnight so the pipes don't freeze.

Do not turn you water heater up. YOU MAY WANT TO WARM UP YOUR HOUSE IF YOU CAN. Just wait for the thaw. Keep an eye on your pipes. 20 deg. is not that cold for a short time. It may just freeze and block up with busting the pipes. Turn all your faucets on a little if you are going to be home to keep an eye on them. Flowing water is hard to freeze. While you are waiting, locate you water main shut off if you don't know where it is at.

Everybody should know how to shut off all their utilities, gas, water and electric. I would say anyone over the age of 10-13 years old and up.