Would black holes be present in all dimensions? I'm watching a video about string theory, in which the fact that gravity is weaker than the other forces is explained in that gravitons aren't bound to our universe directly, and can flow across various branes. If this is the case, would that not mean that singularities would be like fixed points across the various parallel universes?
Link: https://youtu.be/l5t8STlF_ns?t=19m59s
 A: 
Would black holes be present in all dimensions?

If you mean whether there can be black holes in higher dimensions, yes, people do calculations about that all the time, see, e.g., this paper by Emparan and Reall.
In general, black holes in String theory might be something like a black branes or not even be singularities, but rather, e.g., "fuzzballs".

singularities would be like fixed points across the various parallel universes?

Maybe. Similar stuff has been proposed before, e.g., that apparent black holes might actually be wormholes to other universes.
A: Not in general. Already in the low energy string theory, that is supergravity, singular solution in a lower dimensional space can lift to regular solutions in a higher dimensional space.
In particular, singularities covered by horizons in 4 dimensions, that is black holes, can lift to smooth and horizonless solutions dubbed fuzzballs. The extra dimensions regularize the singularities, replacing it with a smooth manifold. You can have an intuition of this process by lifting 4d to 5d: in radial coordinates you could have an extra compact coordinate that is shrinking while going near the region of the would-be black hole, capping off smoothly.
On the other hand it is possible to have singular solutions in higher dimension, for instance the  Schwarzschild black holes generalize in Nd trivially to a Schwarzschild-Tangherlini solution, with a singularity and a N-2 dimensional hypersurface horizon.
