Mostly wrong, and even the parts that a right, you make far more confusing than the need to be. I think you're using your maze example to try and represent branching within the algorithm and only confusing yourself. How would the maze for multiplying two numbers together (a P algorithm) look different from the maze for the satisfiability problem (an NP-complete algorithm)? I really can't picture your maze for either of them.
As far as your nondeterminism allowing you to simultaneously try each path, make copies of yourself, etc. It's just confusing, it makes NP harder to understand, and really clouds what's actually going on. Look at it this way. Nondeterminism allows you to always choose the correct path. Every branch you come to, you have the magic ability to pick the correct path on the first try. I call it a magic ability, you call it a super power. Forget about trying to understand how you're trying all paths; the whole concept is a mathematical model, so why inflate it with bloat trying to explain something that need not be explained?