The knob and push pull pin are the height adjustment. Loosen the knob and then pull the pin while holding the seat. Set the height and tighten the knob which stops any wiggle of the pedestal.
There has to be one control to loosen the rotation collar to turn the seat. The seat has a split collar that when tightened, grabs the pedestal. In that mode, it doesn't rotate. Some seat bases have knobs and some have a lever but in both cases those are connected to flanges on the split collar with a threaded shaft. Sometimes that threaded shaft and nut freeze up but your hardware is pretty new and shouldn't be like that'
If the seat can be rotated at all, you should be able to lift the whole thing up and off so that you can get a better look at the mechanism.