Everyone covered your questions pretty well except for the topic of creative thinking. Allow me to offer a slightly different perspective.
You WILL NOT be allowed to "rewire" the reactor to increase reactor power. I remember when I went into the Nuke Navy I had visions of Capt. Kirk calling down to Scotty telling him to bypass the Dilithium Crystals so that they could restore warp drive. Needless to say, I was disappointed about that part. You will memorize the correct Navy Nuke definition of every word and term, the correct Navy equation for every problem, and the correct navy answer to each question. There will be volumes of procedures and requirements that you will be forced to strictly adhere to during the performance of any and all tasks. So, are you going to get many chances to re-engineer something? No.
However, that's only one small aspect of the application of creative thinking. There's plenty of room for creative thinking in the Nuke Navy when it comes to managing time and resources and getting work done [particlarly technical work]. As an officer, your job would primarily be to serve as a manager. Now the root word in manager is manage. A lot of people, including most managers and officers, think that being a manager involves sucking up to the next highest people in the chain of command, ordering the lower people around, and thrashing people when things don't work out the way that they thought that they should have. This is a terrible misconception that many learn, apply for a lifetime, and take to the grave with them, particularly in the Navy.
A real manager manages. He manages time, resources, people, personalities, regulatory requirements, operational needs, morale, and, above all else, the strengths and weaknesses of his subordinates and superiors. Managing all of this also involves a lot of problem solving of complex technical issues intertwined with the ever-present network of requirements that you must meet. So, no, we're not talking about business school management type stuff. We're talking about real problem solving to get work done in a highly regulated technical work place. To do that well, there's a lot of creative thinking involved.
Are there officers in the Nuke Navy who are just "yes" men, sucking up to their superiors, pushing papers, doing what they're told, and following procedures? Yes, probably the majority. However, the few who were actually capable of thinking outside the box [but acting inside the box], who looked for the best allowable answer to each question, those were noteworthy men. I remember every one of their names.
As far as exceeding the blueshirts and/or Chiefs in technical knowledge, that's a mirage. There is no exceeding someone else's knowledge. Everyone knows something useful. Can you become technically competent and earn their respect? Yes. Will you ever know more than all of them? No, probably not [or you better hope not, because if you do, then that means that you have a bunch of losers working for you]. The nice thing about working with people who know things that you don't is that you never stop learning [provided that you keep the right attitude].
Good luck,
mgm