No typically you want to use all types of movements in order to control the center of the ring and "move" your opponent.
It depends on your style, if your a rangier fighter then you will circle a lot more. Orthodox v Orthodox its generally better to move to the right, you cant walk on to a big right hand that way. However as said going one way the whole time isnt the most sensible thing, you need to mix it up a bit.
Power hand is usually the rear. If you move to your right and someone tries a lead left hook it will be pretty easy to see coming.
Don't worry about it. Circle whichever way you need to to cut off the ring, escape, or set up something you want to throw. Circling away from the power hand is something that works on ESPN FightNight 2001 or something, not in the ring. Not that it's bad, but you don't always circle away from the power hand as a rule. That would be letting your opponent control what you do, and in anything conflict-oriented you want to control your opponent, not the other way around. My coach always says "Think about what YOU want to be doing in there, not what the other guy's doing."
Circle when you want. It's not really a thing you should put much thought into, I think. Just mix it up a little bit and don't always, say, circle to your left, your your opponent will time you eventually ALA Joe Frazier-Muhammad Ali. Just mix it up.
move away from the powerhand, well yes and no. I have seen it so many times when they move away from the big right (orthodox) and run right in to a powerful left hook that in a way is much closer to you. Mix it up never be easy to read.
Was gonna reply earlier, i seem to notice in all my time, be it amatuer and pro fights, 99% in general will move clockwise, both fighter regardless of style. Sure they feint to left and right and do go anti clockwise.....but for how long ? Made a thread a while back, truly interests me.