Do pets typically view their human owners as a much more powerful being than them? ?

Who really knows.   However most pets (dogs) prefer to keep their owners happy for their own good (they prefer a stress-free life) so they learn to fit in with what 'mum' wants.    Rather like a sig.other!!

My dog thinks I'm a wizard. I can control whether its light or dark, hot or cold. I can make a thunderstorm appear instantly (with help from youtube) and make it go away whenever I want. I can make people bring me food whenever I want. And I have and endless supply of water and food for them. 

Only if their owner fails to train them

Most pets are smaller than their human owners.  Even if they are not, the human will be dominant over the pet.  Dominance isn't just a matter of size.  It is also a matter of supplying what the pet wants - such as food, shelter, and companionship.

Well, they see us as the pack leader, so I guess so.