I'm using custom sky textures for Donner right now. Is it possible to make that skin specific for Donner only, and not on maps like Sora and such?

Also, what does $keyword do?

if the sky name is the same in all of those maps, then they need to use the same one. you could embed a custom sky with the duplicate name into a new map without causing any conflicts, but altering any existing maps would most probably fail with a 'conflicting versions' error when you try to join a net game.

the texture browser in hammer has a filter for the $keywords that are set in vmt files. say you made a bunch of textures with unrelated names; brickwall_pink, basewall_blue, window_green, stairs, rooftiles_orange etc. these names don't have any common denominator, so you can't type anything in the texture browsers name filter to show them side by side.
but if each of the above textures had "$keyword" "mybadtextures", in the vmt file, then typing mybadtextures in the 'keyword' filter of the texture browser would display all of those textures together.