The only thing currently known for sure about dark matter is that it reacts with luminous matter gravitationally. I think we can say with a very high degree of certainty that it doesn't react with luminous matter electromagnetically, or via the weak or strong force*. Which is why it's called dark.
So anything that experiences gravity will be subjected to the effects of a black hole in the same way as 'normal' matter.
*More accurately, it's safe to say dark matter doesn't interact via electromagnetism. I don't know if the others have been positively ruled out. Weakly Interacting Massive Particles were ruled out as a candidate for DM a few years ago, if I recall correctly.
No, Dark Matter cannot interact via the strong force or electromagnetically because it implies it has either color charge or EM charge. Color charge is easier to detect than EM charge because it has much higher interaction probabilities, and EM charge would be easily observed because it would interact with photons by its messenger particle.
The weak force however, is a possibility that they can interact with, because it is so weak and short ranged. However, it is not observed to, otherwise we would have had headlines with a direct detection report already. They are currently trying to do so with a variety of experiments.
WIMPs on the contrary are the only "realistic" candidate left for DM, unless if I am mistaken (source?). The only things ruled out are MaCHOs (Massive Compact Halo Objects), Neutrinos*, and MOND (Modified Newtonian Gravity).
MaCHOs can be detected via gravitational lensing events of passing stars over background galaxies/other stars. These are not observed nearly statistically enough to have evidence of it as Dark Matter.
Neutrinos are ruled out* because they are too light to account for the DM fraction, as well as being too relativistic to account for the observed galaxy simulations.
MOND is ruled out because they need to be fine tuned to specific galaxies, and no individual MOND theory can adequately describe the observed phenomenon over all observed galaxies, so it is highly unlikely considering how many additions need to be done in order to make it sorta work.
*Sterile Neutrinos, which is a 4th generation neutrino which does not interact at all except for gravitationally is not quite ruled out, but it is a rather hideous addition to the model. Using Z boson decay resonances, we have ruled that only 3 generations of matter exist, assuming the lightest lepton is less than half the mass of the Z boson, or 91 GeV. It is possible that the 4th generation neutrino is greater than 45.5 GeV in mass, but such a jump from ~ 1 eV with differences of 0.1 eV of the other neutrinos to suddenly >45.5 GeV is unreasonable.