Is there any lotion, cream or anything that I can use to keep my face and ears warm?I cannot be wearing earmuffs of any thing like that. There's no location in the office that's better than my current one.
Sounds like you may be a bit overcautious but its better to be that way then not being aware. The danger of old furnaces is that the heat exchanger sometimes cracks and allows products of combustion to get into the plenum that supplies the warm air to the ducts. Check with the gas company as I believe its mandatory that furnaces be inspected every so often especially in rental properties. If there is a dangerous problem they will simply turn off the gas until its made right. In the mean time get a carbon monoxide detector and place it close to where you sleep. As carbon monoxide is just about the same specific gravity as normal air you can plug it in any socket that's handy. And I assume you already have a smoke detector in working order.
Laws vary depending on where you live, but generally I'd say that would be likely to be illegal since it can cause a hazard for bike riders, pedestrians, animals, etc.
What I usually do is get a trim at the salon. Don't EVER pick at them/split the hair because that'll make it worse. After trimming them what you should probably do is find a good conditioner like Panteen Pro-V or Sunsilk because those are the ones I like and use. :)