Is it possible to extend spotlight's search feature to support additional commands?
For example, is it possible to define custom web search aliases, meaning I could type yt and it would provide results from youtube.
Alternatively, is it possible to add additional system commands were I could type sl (or some variant) to put my computer to sleep.
No it is not possible, there are only 4 types of extensions for OS X Yosemite:
Today - Get a quick update or perform a quick task in the Today view of Notification Center
Share - Post to a sharing website or share content with others
Action - Manipulate or view content within the context of another app
Finder - Present information about file sync states directly in Finder.
All of these extension types are explicitly activated by the user for functionality. Apple has said that they are just getting started with extensions and plan to add more in the future, so logically it seems that Spotlight extensions are next (goodbye Alfred :sadface:).