Yes. If you want to lead projects, develop applied methodology, or do actual statistics, strongly consider the PhD. The PhD will open research-oriented jobs that the Master's may not. Research does not necessarily mean academia. You can certainly do this with a Master's, but you're less likely to be given the opportunity and more likely to work as an analyst or as support for the PhDs. This might be something that interests you, as you might work more closely with data and the nitty gritty details.
Probably depends on the industry of interest. They may be different doors. Statistics has the potential to be a bit more "general" than the other ones you mentioned, which may mean it opens more doors. On the other hand, the right Operational Research PhD is likely to involve at least some background in statistics that you can leverage to get your foot in the door for some of the statistics jobs.
Yes. An undergraduate degree will prevent you from advancing unless you can find your way into management. No one really cares that you won a prize in Number Theory as an undergraduate. Some don't care about anything at all that you did as an undergraduate. A PhD does not guarantee advancement, but it is much more likely . A Master's will hold you back from certain areas where the credential (and requisite background) provided by the PhD is generally required, but given enough experience you can also make your way into those areas eventually. You are much less likely to get there with only an undergraduate degree.
That's up to you. If you aren't sold on research, a research-oriented Master's degree might help you decide whether you would like to pursue a PhD without the time investment of a PhD. A taught masters can be good for a terminal degree because it gives you broader knowledge/background when applying for jobs. It also means you could step into a PhD with enough background to jump right into research. In North America, my understanding is it usually means you're not going to get into a PhD in Statistics.
If money is important, you might find a better return on your investment if you get a Master's and start working rather than putting in the extra 3 years to get a PhD. On the other hand, those extra 3 years may balance out within 5-10 years, depending on the salary you can pull in after you finish. The value of the knowledge and experience of the PhD is something only you (and human resources managers who don't have any idea of what is needed for the job) can evaluate.