How hot air balloons fly: because the hot air inside the balloon is less dense than the air outside of the balloon. The principle is really very simple; hot air rises and cold air sinks.
The physics of hot air balloon flight or how a hot air balloon fly whilst quite simple is often poorly understood. This article includes links to several published articles on hot air balloon physics.
Commercial Propane is sometimes supplied as a mixture of propane and other Liquifed Petroleum Gases (LPG) such as butane, butylene and propylene. Autogas, in most parts of Australia, is a mixture of LPG gases including propane. LPG mixtures can be used as hot air balloon fuel provided adequate fuel pressure can be obtained.