The slider that I mentioned, locted above and to the right of the timeline, does not vary the duration of the clip, but only expands out the display of the clip on the timeline to make it easier to edit. Are you referring to dragging the edge of the clip?
You cannot increase the duration of a video clip by dragging its edge. The duration of the movie is what it is. You can increase its playing time by slowing down its speed, but then you get a slow motion effect. You can, however, reduce the duration of a video clip by dragging its edge to trim out some of the footage. But that would result in some footage being removed from the clip. You can also speed up the clip to decrease its playing time.
I don't know why you would be needing to use the < key or the > key. Those are keys on your keyboard and would not need to be "displayed" in any event.
You've made a good start by creating a project and importing your clip into the timeline. It appears that you want to split the clip into segments to edit them. You can do that by placing the playhead at the in-point where you want to make a split, and do Modify/Split clip. Then move the playhead to the out-point and do another Modify/Split Clip. That will create a segment between the two split points that you can delete, or move to a different place on the timeline, or apply edits.
Refer to the help menu link that I posted earlier. It has a good search feature where you can search by search word or by subject matter in the sidebar. That's a good way to learn the basic features of iMovie.
-- Rich