Indeed, as Florin said, dark matter interacts with normal matter via gravity, so it has the first two for sure. It is one of Einstein's core axioms that those two are identical, universe-wide. So numbered question 2 is based on incorrect premises, and not really answerable at all. Question 3's premise is semi-incorrect, insofar as it implies some special kind of inertial mass for dark matter, when it's really just regular old inertial mass.
The most popular theory of dark matter currently is "WIMP"s- weakly interacting, massive particle. That "weak" doesn't just mean weak in the everyday, non-technical sense. It means that WIMPs interact not just via gravity, but also via the weak force, i.e. the one responsible for radioactivity and whatnot. There is also some theoretical work done on "Super-WIMPs", which is an awful, awful, misleading name. They got the name in analogy to WIMPs, but in fact Super-WIMPs are postulated to interact only via gravity, so the WI in their acronym is totally inaccurate.
I think the state of the art on WIMPs and Super-WIMPs is that they are not composed of baryons, and so would not fall under the third category of mass. (By the way, nobody has detected any WIMP or Super WIMP directly, or even given a cogent statement of WTF they actually are. All theories related to dark matter are at this stage prima facie TOTALLY ABSURD AND PREPOSTEROUS, and their only selling point is that in the eye of most beholders, the alternate explanations are even worse. Physics is really in trouble over this. Everyone is praying for deliverance from the LHC.)