The Ordo Xenos have their own Marine detachment, the Deathwatch, who are drawn from pretty much every chapter.
The Ordo Malleus have the Grey Knights to call on.
The Ordo Hereticus don't have Marines, but they do have the Sisters.
The Inquisition as a whole has mixed relations with different chapters. The Space Wolves wouldn't be real popular with them, after the First War for Armageddon, and what went on after.
The last thing the Dark Angels (and to a lesser extent their successors chapters) want is the Inquisition poking around their history, and finding out about the Dark Angels terrible shame, and the Fallen.
Some chapters they get on well with, some .. not so well.
If you mean this video though
That's a Grey Knight, not an Inquisitor.
The Inquisitor in this one
is wearing power armour, by the looks of him, but non Marines can wear power armour.