Welcome to the BA forum, I'm sorry that your first experiences are so negative and I hope you stick around long enough to put in some better reports in the future, since this group is always good value, if you can cope with a few oddities.

I fly BA a fair bit and your experiences are pretty rare - basically turmoil at short notice and very few resources to deal with them. I have been there myself, but 3 times in over 500 OneWorld sectors in the last 2 years, about two-thirds on BA. So while not trying to justify the chaoas you faced, it is difficult for any organisation to set up a coping mechanism for a relatively rare event.

In terms of compensation, you will have seen the EU's guideline. My suspicion is that you will struggle to get that simply because all airlines do their damnest to avoid it. I am afraid that I think BA will prove difficult on the EK ticket too (they are very iffy about rebooking on alternative providers, even if you are a Gold member), but on both points if you politely persist and insist, you should get it refunded/compensation eventually. However I have to say that really this is the point of good quality travel insurance, particularly if you travel regularly. It shouldn't be that way, but I describe the industry as it is, rather than how I want it to be.

Having got landside, you don't appear to have gone to the BA ticket/check in area? If so, this may cause you difficulties, since they may have had a process going there to rebook people. I accept DXB is a bit of a zoo, but that would be second port of call (first being a phone call to BA Reservations).

Again my commiserations for this poor experience, and I really like the way you put it in perspective. You are absolutely right, we in the middle class West have no idea how lucky and comfortable we are in comparison to most of the world.