Solo only. Duo and fireteam runs should be able to easily reset to a fresh instance with alternate characters.
Scroll wheel is singled out from other buttons or keys (on keyboard, mouse, or controller) due to the fact that it allows the user to register multiple inputs in rapid succession - faster than the user would be able to input those actions if they were using any standard button or key. The intent of the rule is to prevent using scroll wheel in situations where quick successive inputs would give the user an advantage in performing that action over someone who is doing the same action with a typical key or button.
The most common in-game action where quick successive inputs gives the user an advantage is when scroll-wheel is bound to "Jump" (titan skating, etc.). Some less common unfair advantages of using scroll wheel involve binding it to "Bring Out Ghost" (to perform ghost skips faster) or binding it to "Fire Weapon". Typically any in-game action that requires the user to hit the same key/button twice (in rapid succession) cannot be bound to scroll wheel.
In regards to the specific questions in this thread - "Class Ability" and "Switch to Power Weapon" can be bound to scroll wheel without violating anything I mentioned above, as there is no benefit to inputting either of those actions in rapid succession.
Scroll Wheel Click acts like a standard key or button and does not offer the same benefits that the Scroll Wheel itself offers, therefore it does not matter what in-game action is bound to Scroll Wheel Click.
Let me know if I need to clarify any further - cheers.