What materials can Kitty Pryde not phase through? Could she phase through adamantium? Please provide citations to back up your answer to each question.
Marvel Universe explains Kitty's powers:
And continues regarding the limitations of her abilities:
Marvel Wiki expands on this:
The closest limitation to her power that would prevent her from phasing through adamantium mentioned might be the density of adamantium, but as discussed here, adamantium is not particularly dense.
The density of the material is the only known factor preventing her phasing ability. There is no evidence that Kitty Pryde would not be able to phase through adamantium.
In fact, during the Enemy of the State storyline, she successfully phased as Wolverine lunged, resulting in Northstar being stabbed.
In the TV show Spider-Man and his Amazing Friends episode "The X-Men Adventure", Kitty Pryde is placed in a cell made out of Vibranium, a substance that is evidently able to block her phasing powers.
In Kitty Pryde and Wolverine #6, we see Wolverine stab straight through Kitty Pryde who is temporarily phased.
As to what materials Kitty Pryde can pass through, Kitty is described by the Marvel database as having more difficulty phasing through denser materials.
Since Osmium is considered to be the densest element, since Colossus is described as having skin comprised of an "ionic form of osmium" and since Kitty can phase through him with relative ease, it follows that she can phase through any non-magical/non-force-field-based substances with the exception of Vibranium.