Well a few things.
1) Your original post, tl;dr, but I have a comment on the Dyson Sphere concept. The popular concept of a massive structure completely enclosing a star is not what Dyson came up with, I fail to remember who warped his idea into what most people think it is.
A true Dyson Sphere, if I remember right, is just a (really really big) network of solar power collectors distributed in a... a spherical pattern around the star? I think that's right. God forbid I just look it up on wikipedia. But anyway, it wouldn't be a colony structure as far as I can tell, just a humongous source of power.
It is not a solid structure, but a whole bunch of small ones.
The Niven Ring does seem to answer the problems with the popular version of the Dyson Sphere concept though.
2)
tbh, I've never thought of that.
But I have seen artistic concepts of black holes where part of a nearby star is sucked around into a circle before going inside the black hole and I figured those artists worked out the physics part before doing the image to make sure it was correct.

if this star is going to blow up, be sure to let me know.
There are a number of things that may be, coming from my very limited astronomy knowledge, and I'm probably very, very wrong on some parts.
1) A binary star system in which the larger star has expanded beyond its (I forget what it is called) radius and material has started falling into the smaller one (hence the disk). The smaller one is likely a white dwarf and if it collects enough mass, boom. The white dwarf can't burn it away because white dwarves do not undergo fusion.
2) Same as above, but the smaller star is a neutron star (I *think* this happens now and then). If it blows up, I think it would be from the big star burning itself out. It would have to be a pretty good sized star, too.
3) Smaller "star" is indeed a black hole. I am even more sure that this one won't blow up, simply because I haven't heard of anything about black holes blowing up.
Maybe the larger star's life is shortened by lighter elements being sucked out of it faster.
I can't remember what happens to it and I miss having my astronomy book, I should not have bothered to sell it... partly because I didn't get jack crap for it. Only like 7 bucks which bought me a cool mechanical pencil.
Then again, books are outdated almost if not just as fast or faster than computers are.