Why would that be true? Individual gas molecules manage to disk-ify and turn in to planets, I don't see why a black hole couldn't. This would presumably happen in the early stages of system formation when there was a lot of stuff flying around separately.
However, more broadly speaking, the angular momentum is conserved, so the result would be more or less the same. However, given the enormous, ridiculous difference of relative masses (and therefore angular momentum) in the case of black holes and some gas particles, I think my initial point stands.
Yes, conservation of momentum is the right way to think about that.
So you’re saying you’d expect a body that were captured at an arbitrary angle to end up orbiting in the same ecliptic as the planets roughly around the sun’s equator?
I don't think this is true. Plenty of (almost everything) things would interact with the black hole's gravitation but not be close enough fall in.
What makes you think that a black hole orbiting the sun is a "planet" by the definition you're using?
More generally, you can't prove things about the physical world just by citing somebody's arbitrary definition of a word.
I would have thought that any model of a black hole in this scenario essentially approximates one of those conditions.