Regarding the gearing, as the turbine blades rotate at something near 20,000 rpm, if there was no gearing to the prop then ..well it doesn't bear thinking about. The 12ft diameter prop on an ATP for example, rotates at a maximum of 1200 rpm, anything faster and the prop tips would be supersonic and inefficent.
A Free turbine engine, such as the PW126, has no direct connection between the hot part of the engine and the prop. Simply put, the prop is driven by a turbine that sits in the jet pipe, rather than via a gearbox off the engine itself. You can run these engines with the prop stationary and use them as an APU.