If the power turbine isn't connected to the compressor, what is it connected to?
It would be connected by a shaft to the......power gear train and thence to the propellor or drive shaft.
If the compressor isn't connected to a turbine, what is powering it?
I'm pretty sure it is connected to a turbine, just not the "power" turbine. I suggest you may want to buy a good reference book, one I like is Rolls Royce the turbine engine