The Force 2005,

1. Hurricanes undergo eyewall cycles as a natural part of their development. We don't know everything behind them other than that they occur and our conceptual/mathematical models say that they should occur. How often, exactly when, what the end result will be -- all things we don't know.

2. Storms do not always rapidly intensify after the completion of an eyewall replacement cycle. Generally, they weaken during the cycle and come back to their initial intensity afterward given the same underlying conditions. If those underlying conditions change, however, as they did quite drastically with Katrina -- dry air mixed out, approached the Loop Current -- then you can see further intensification, sometimes at a rapid pace. Other storms will weaken after an eyewall cycle due to land interaction or poorer environmental conditions.

3. Distance that the winds extend from the storm isn't related to the strength of each side of the system. The forward motion of the storm is going to lead to that right side being a decent bit stronger, whether near the center or far away, due to additive/subtractive effects on the right/left side of motion.