Can you use propane gas instead of natural gas in gas stoves?

In many of the cases, you can use propane or natural gas for a gas stove. However, since natural gas is based on a different chemical element (methane), some adjustments have to be done. In particular, the orifice (an opening that controls flow of gas) has to be changed to allow higher heat flow. Be careful though, some gas stoves can work only on one type of gas, propane or natural gas. You should always consult with the manufacturer before doing any modification and any changes should be done only by certified technicians.
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Which fuel, propane or natural gas, burns better and hotter?

Propane is hotter. It is one of the component of most natural gases and product of refinement of crude petroleum. Propane heat output is about 2,500 BTU per cubic foot. Methane in its turn is the main constituent of natural gas and its heat output is more than twice less than propane's - 1,012 BTU per cubic foot.
Are we going to run out of natural gas soon?

Not in our lifetime. Natural gas is produced from oil fields and natural gas fields. A recent discovery of the world's largest gas field in Qatar (Middle East Asia) is estimated to have 25 trillion cubic meters (900 trillion cubit feet) of gas, which is enough to last for more than 200 years at optimum production levels. Eventually, we will run out of all fossil fuels, including natural gas, but by that time and hopefully even before that, some alternative fuel will be discovered.
How much gas do you need to heat up your house?

This question is tricky and will depend on too many factors: where you live, how often you heat, what's your house built from, what kind of insulation, etc). Nevertheless, if we take 6-month season of heating, you can say that you'll be probably using about 500 hours. Now, you can take the heat output of your gas stove (say 50,000) and find the total heat output you need: 500 x 50,000 = 25,000,000 BTU.
Now convert it into therms for natural gas (~300 therms) and multiply it by the gas cost (~ $1.50/therm) = $400 for a season. Or convert it into gallons for propane (~330 gal) and multiply by the gas cost (~ $2.00/gal) = $660 for a season.
You can have a look at
this Fuel Comparison Table to check cost effectiveness of different types of fuel, including propane and natural gas.