Are taxiways always one-way towards a specific, fixed direction?
At any given moment they are generally one direction as planes cant really turn around like cars but the taxi way its self can typically support traffic in either direction. Airports do have a "flow" to them but it depends on the runway they are using as well as the direction of departure of that runway. If the wind shifts and the approach is taken from the opposite direction the controllers will "turn the field around". 

This time-lapse video shows the principal pretty well, the aircraft are pushed out onto the ramp form the jet bridge, nose towards the taxiways. They then head out to the departure end of the runway all following generally the same path. They queue up and depart when cleared. If the wind were to shift around they would do so from the other end of the runway which would reverse the flow (generally speaking) on the field. 

You can find the FAA's advice on designing taxi ways here.

At uncontrolled airports the pilot can turn the field around.