J just got out of the Navy after joining through the NUPOC program back in 2011. So to answer your questions...
1. There's 3 positions you can apply for through NUPOC: Naval Reactors Engineer, Power School Instructor, or Nuclear Line Officer (Submarine or Surface)
Naval Reactors is probably the closest to a normal civilian engineering job. You get commissioned as an officer in the Navy, but you work in Washington DC helping design reactors for the Navy. This is the most difficult job to get into (they are extremely selective), I've heard it can be pretty tough, but you're going home every night. After 5 years, you are separated from the Navy and may continue to work for Naval Reactors as a civilian. This should provide very valuable engineering experience and should serve you well in an engineering career even if you decide Naval Reactors isn't where you want to be long term.
Power School Instructor is definitely the easiest out of the three. After you commission you spend your 5 years in Charleston, SC teaching nuclear power and engineering concepts to nuclear operators (officer and/or enlisted) as part of the training pipeline before they are stationed on a ship. After your 5 years, you most likely will separate from the Navy unless you can laterally transfer to a different community. Usually an officer community doesn't want an O-3 (your rank after 5 years) that they have to train from scratch however. The job doesn't require any engineering knowledge (they will teach you everything you need to know before you actually start teaching), but you will be giving lectures, grading homework, and administering tests. You usually aren't well respected however since you won't be stationed on a ship and you'll be dealing with people who either have deployed or will be deploying.
The third job is to be an Unrestricted Line Officer either on a submarine (which is what I did) or a surface ship. As a submariner, you will be dealing with nuclear power from day one. You'll learn nuclear power concepts at power school, learn how to operate a nuclear power plant at prototype, and then spend about 3 years stationed on ship where you will be going underway, deploying, and standing duty. You will be put in charge of a division in which you will be responsible for their performance. This will require more people skills like motivating and coaching and less technical knowledge (the guys that work for you will most certainly know more about their systems then you ever will). Where the engineering comes in is mostly when standing watch as an Engineering Officer of the Watch or Engineering Duty Officer. You will be put in charge of supervising the nuclear reactor and ensure that it is operated properly. You will also learn the tactical elements of the ship and get to drive the ship as the Officer of the Deck. It's definitely not like a civilian job in the slightest.
2. After you commission (so after you get through Officer Candidate School), you will make O-1 base pay which you can look up online. Right now it is about $3000 a month. You will also get a food allowance (BAS) and a housing allowance (BAH). BAS is about $230 a month tax free and BAH can be anywhere from $900 a month up to $2700 a month depending on where you live. ($2700 a month is pretty much only if you get stationed in Hawaii.) You can look up online what your BAH will be based on zip code. If you go submarines, you will also get submarine pay even while you're in training which is about $300 a month. You're starting pay right out the great isn't that great, but you do get promoted to O-2 after being commissioned for 2 years and get O-3 after 4 years as long as you don't get a DUI or something equally terrible. Time in the NUPOC program also counts as time in service so that will help as well especially if you get in early. The pay for all three jobs will be identical with the exception of BAH. As an O-3 line officer in Hawaii, I was taking home about $100k per year (after taxes). Hawaii can be pretty expensive to live in, but if you're ok with roommates you can pocket a lot of money. There's also a $30k per year retention bonus for line officers after your 5 year point if you sign on to do at least one more tour. I'll just say it wasn't enough to keep me in the Navy.
3. I can only speak for the Line Officer job, but the work was very challenging and stimulating... at times. It was definitely a unique experience that could not be replicated anywhere else. I will say the military is a place of extremes. The job was either extremely exciting and/or challenging, or it was extremely boring (standing 8 hour watches doing absolutely nothing.) The first time I took a submarine to periscope depth or drove it on the surface as a qualified OOD were some of the coolest moments of my life. The next couple hundred times..... not so much.
4. The Naval Reactors position will help you immensely in an engineering career. The power school instructor may help you with teaching or training positions but will help you the least in your future career. The Line Officer position will be extremely beneficial if you want to go into an operations or management position, but will provide little if you want to go back into a professional engineering position.
I didn't make the Navy a career, but I'm happy I did the time that I did. It's an experience I'm much more appreciative of now that it is over. Hope my input helps.