Also, would you say the outline is black? I've always been wondering whether I should use pitch black, or some kind of a dark tone that fits with the overall character design?
When you're talking about the darkest pixels of the outline, it seems to be pitch black (0,0,0) indeed (the outline surrounding that girl character's gloves for instance). But then you have parts of that girl like her hair, where the outline is of an actual dark color and not just black (with a hue that's analogous to the hair, like a really dark hair color). I personally feel this variation looks way more natural than using black for all outline pixels.
I understand this as "Selective Outlining". I certainly don't have the groundings to explain it, being very inexperient with pixel art, but the effect is explained in the following article. Search for SelOut on section IV. Things to Avoid:
(If you're interested in the craft the rest of the article is a great read, too.)
The science behind SelOut (or "outline breaking" as it's also called) has to do with the visual sensation of expansion or contraction of shapes based on a light-to-dark contrast.
These great tutorials explain a bit: