Re: Perhaps someone can explain something to dumb old me.
Nothing propagates across the event horizon. In particular gravity does not propagate across it. Rather the gravitational effect of a BH is essentially a sort of 'scar' left as the star collapsed: it's a record that there is some mass there – perhaps, better would be to say that the gravitational field is the mass, although that's not quite correct.
However this isn't really right. One important thing to understand is that, with slight caveats, the gravitational field (and hence the spacetime) outside some suitably-symmetric massive object is, to use a mathematical term unique. What that means is that, no matter what is going on with the object the gravitational field outside it is unchanged. The slight caveat is that the spacetime should be 'asymptotically flat', which means that, far from the object, everything settles down to Minkowski space: this isn't true on cosmic distances (there are, for instance, other stars!), but it's a good enough approximation in practice.
What that means, is that, if you imagine some star collapsing to a black hole, then the gravitational field outside where the star was is unchanged: if we used our giant star-crushers to crush the Sun down into a black hole, then nothing would change gravitationally (well, so long as our star-crushers were rather light).
So, in fact, nothing needs to propagate across the horizon: the field outside the horizon is unchanged by the collapse, so long as its suitably symmetric. In particular there's no information that has to be somehow continually emitted from the thing to tell spacetime how to behave: it just does what it always did. The situation is what's called 'stationary' in GR.
I have not explained this very well, I think: sorry.
To answer two other questions.
Changes in gravity propagate at the speed of light: so gravitational waves propagate at the speed of light. Indeed it's really better to think of the speed of light as being the speed of causality: it's the speed at which information about things happening far from you gets to you (or the maximum speed at which it gets to you). That means that nothing propagates across the event horizon because the speed you need to travel to stay still (to not get closer to the centre of the BH) at the event horizon is the speed of light: no information, of any kind, can get out.
(Caveat: what I'm describing is the classical GR picture: quantum gravity may be different, but quantum gravity needs to reduce to classical gravity in suitable limits so it won't be very different in those limits.)
What accretion disks look like is complicated. I think that we are looking at the M87 BH (the one the EHT image is of) from somewhere near one of its poles – so we're looking down onto the disk. And since that's the BH we've got images like this of, well, it is what it is. However even if you are looking at a BH from its equator, what you see is not what you'd expect – a thin line which is the disk. Instead you see something much more complicated, because you can see right round a BH, as light can orbit the BH. So, for instance, you can see the part of the accretion disk which is directly behind the object. And indeed you can see lots of copies of it, depending on how many times the light from it orbited the BH before escaping. And this, of course, is what the people this article is about are interested in being able to see.
What you actually see then, is complicated by this huge distortion of the paths light takes. The images of the BH from Interstellar are quite good: they were actually computed by building numerical models of what the thing should look like (Kip Thorne was involved in this, and he knows what he's about), and in them you can see this weird thing where the accretion disk seems to rise up over the central object in a very strange way.
So in a strange sense, you're always looking 'down' on the accretion disk (at least the inner regions of it).