No, it is not safe to leave a propane heater on overnight. Even if you’re using the heater in a well-ventilated space, the heaters can emit carbon monoxide that can lead to fires. Be sure to fully turn off and secure the propane heater before clearing the area. 

Generally, an oil furnace is considered safer than a gas furnace for several reasons. While both types of furnaces can produce carbon monoxide, a leak in an oil furnace is easier to detect due to the smell. Oil furnaces also don't connect to a gas pipeline, which reduces the chance of a fuel leak. Most importantly, heating oil is not combustible, whereas natural gas is highly flammable. This means there is a much lower risk of combustion or explosion with an oil furnace. However, an oil furnace can still pose a fire hazard if it tips over.

As with any smoking appliance, a smoking oven is a concerning fire risk. It also negatively impacts your indoor air quality, which can put vulnerable people at risk of breathing problems. A dirty oven can catch fire if you don’t stay on top of regular maintenance, so remember to check your oven for signs that it’s time for a cleaning and remove buildup every three months to stay on the safe side.

No. Removing the cause of concern will only lead to deeper concern. You cannot use any fire-powered appliance like a fireplace or furnace without an escape route for the smoke and fumes. If you remove the flue intending to repair or replace it, you should only use the fireplace, wood stove, or furnace once the flue is in working order. If you cannot replace the flue you have removed, call a chimney repair professional immediately.