Natalie has given you some solid gold answers. Here's my 2 cents worth too.
1) Yes, that kind of transition is relatively common. Most people come from a design or digital background, but the business/project angle brings a lot of people too. You're definitely not alone. A background in Business with some project management experience sounds like an excellent start. The side project in tandem with the 6 month course will fill the most fundamental gaps. A realistic timeframe for you to get started is pretty short - a few days would be enough for you to be able to apply the basic practices and principles (iterative, user-centred design, etc). It's all upwards from there. If you can demonstrate sound knowledge of these, backed with some evidence such as a portfolio of your side project, then you may be able to land a position that has UX responsibilities (perhaps a role that also shares one of your strengths in business or project management skills). However, a dedicated UX role would need some solid experience and evidence.
2) As much as I would like it to look like it does now, I can see a few possible changes as things mature. I think neither business appreciation of user-centric techniques nor the expectations of customers will go away any time soon. Much of the design thinking legacy UX inherits or operates within has been around since the inter-war period, so it's not so much a peaking fad as much as part of the evolution of (predominantly digital) design. With your idealist hat on you might expect:
* An increase in dedicated UX roles as more companies and organisations actively engage with UX
* An increase in the number of people transitioning into UX roles from related roles (and conversely leaving UX for other roles)
* People entering specialist UX fields directly from tertiary level education.
* A broader expectation by employers that people working in digital design and customer-facing roles have some experience in, or good awareness of, UX. It might be fair to say that digital designers of all kinds will increasingly consider business needs and a user-centric approach in general.
* Similarly, people that 'build' stuff will both generally broaden as well as narrow their skill sets - freelancers and niche employees will have better capabilities (and higher client/employer expectations) across smaller projects. Developers will have resources and skills that might cross well over into traditional 'design' territory, allowing products and ideas to get out to the world quicker. But also narrower: industries and companies will continue to develop their own expectations around skill sets that are deeper or more advanced in particular fields.
* Further specialisation of UX roles, particularly within industries, ie UX research
* A spreading of the UX salary bell curve as employers get more discerning and the range of UX skill sets and experience gets broader. Essentially: excellent UXers with a good track record will probably continue to earn a good salary. The bottom may open up as employee competition and employer expectations increase, driving some salaries down from where they are now.
3) To add to Natalie's points (and not counter them), even over the past 10 years web design has been getting more complex than HTML/CSS/jQuery. At the moment they're probably a bare minimum for anyone going anywhere near web interface design. All the related libraries and technologies that branch out from these, including things like Git, are going to be useful skills for both freelancers and people working in roles next to developers. I would say coding skills are going to be pretty important for the foreseeable future (20 years at least?) as the world grows and takes better advantage of computing. I kind of think of it as part of being digitally literate, not an optional skill - for people working as 'builders' of digital things at least. I'm definitely not saying UXers all need to be programmers; we just need to have a decent understanding. We'll see a massive skills shortage of programming ability over the next decade or two. Currently the number of Computer Science graduates is diminishing, not increasing as it probably should. Code.org has some great arguments for this stuff.
4) The role you transition into first will be very much related to the one you're closest to as it's very difficult to jump into something you're wholly unfamiliar with. For each of developers, graphic designers, product owners, filmmakers, business analysts, etc this will be completely different. To answer your #4 question directly, and assuming you're working solo or in small teams, I would suggest that you do user research AND design iterations regardless of your actual role. I agree with Natalie's suggestion that you start general and get experience across things before you choose a specialty. Some people go as far as to try and get work in agencies, where even the types of projects are broad too. However, if you could only choose one, I'd suggest the user research option as thats where the real learnings stem from.
5) Check out my article on UX Matters: Beyond User Experience: Onward and Upward Beyond planning your career from generalist to specialist (if that's what you want) I think it's going to be difficult to map out exactly what opportunities or new interests you'll have in 5 years time. At the moment things aren't terribly restricted, and I think (and hope, for UX's sake) that it'll be that way for a while yet.
I hope that helps!