I have a nuclear engineering degree, and was SRO licensed at a BWR. My advice:
1. Operators operate, engineers tell operators HOW to operate
(engineers typically define what the operating limits such as pressure, temperature, flow, system lineups, preventative maintenance frequency, etc. are for the various systems and components)
2. To some extent (reactor physics, thermodynamics, heat transfer, fluid flow)
3. Agree, but engineer pay isn't shabby (we have a bunch of engineers making $120k+ at the plant I work at)
4. I would argue for Mechanical over either Electrical or Chemical, and for an engineering degree over a technology degree.
5. Due to the tight job market, and high wages, many entry level operators DO have degrees (including engineering degrees).
Also, be aware the lifestyles of the two, at least in the US, are vastly different. Operators typically work rotating 8 or 12 hour shifts (including holidays, kid's baseball games, etc), while engineers typically work a more normal M-F day job. Both work schedules have their pluses and minuses, but they can have a vastly different impact on your family life.