furnaces run on fuel-either oil, nat gas, or propane. and yes if you have a propane furnace, then you need propane to operate it and provide heat.

don't know what you mean when you refer to dual heat-are you referring to dual fuel where you have a furnace paired with a heat pump?

IMO

The Ruud Achiever is a gas furnace so you'll need gas (either natural gas or propane). The WarmFlo is an add on heat pump stage that provides A/C and heat using the gas furnace when the temperatures are too cold for it the heat pump alone.

Yes, the air from the heat pump alone will appear cooler than if the gas furnace is running as well. It's more efficient that way. Is the house heating up OK?