The counter balance is not working correctly, but repairing this or replacing it is non-trivial. Instead, you can pickup a device like this that will create enough friction to hold the window in place. It should be installed between the window and the frame and is a simple DIY job.
http://www.lowes.com/pd_128860-76018-F+2537_0__?productId=3010767
You are correct that having a hot radiator on what's effectively a cold space - the porch - is very inefficient and, presuming nobody's on the porch most of the time, wastes a lot of energy.
And you are correct that the hot water going into that radiator is being cooled in the process.
However, it is unlikely that the water is going to any other radiators, but rather it's going back to the boiler to be reheated. Nevertheless, you are right that stopping water flow to this radiator will save you on your heating bills.
But - if you stop the flow of water through the radiator, no amount of insulation will keep the pipe from freezing, because with no place for the cold water to go, the hot water in the rest of the system WILL NEVER reach the pipe you insulated. It's just like turning on the hot water in a cold bathroom - the water runs cold for a while even though the hot water is available elsewhere in the house.
On a cold enough day, the stopped pipe with water in it will freeze, no matter how hot the rest of the system.
The best solution to this is to remove the radiator completely. To accomplish this, you need to trace both the input and output pipes for the radiator in question back to an interior space that doesn't ever drop below freezing. The entire system will then need to be drained, and the input and output pipes cut off and capped so that the useless radiator can be removed.
EDIT:
Since you're looking for a short-term, this winter solution, here's what you can do for now to minimize the waste.
- DO NOT TURN OFF THE RADIATOR
- DO turn down the radiator to as low as you can get it without shutting it off. You don't want it to have a chance of freezing.
- Wrap the radiator in blankets to keep in the heat it does generate and conserve energy as much as possible.
Best Answer
Absolutely. Down is a terrific insulating agent. It would work even better if you seal up the edges of the curtains along the window. A good way to do that is with either magnetic strips or velcro along the curtain seams on each side. That way you can let sun in during the day and seal rhem up at night to prevent heat loss.
I assume your windows are single pane. If you want to go a step further you can conserve even more heat by also installing plastic film insulation on your windows. Kits are available online and at most hardware stores.