Final Cut - split clip into separate clips
I'm not familiar with FCPX specifically, but on pretty much every NLE ever made, you either use the razor tool to split the long clip wherever you want or set in and out points on the source window and drag in the clips already shortened.

If you want to be able to use a preset portion of a longer video as a source that you can just drag on, it will need its own timeline.  Put it in a timeline by itself along with any effects or anything you want to apply to it and then you can use a nested sequence in another timeline.