Unaware of a scrollbar shortcut, but if the sequence is in focus it can be jumped from end to end via a mouse wheel capable of horizontal scrolling.
There are many ways to trim clips. If you want to create many discrete clips from a single clip, first right-click the bin clip and COPY. Then right-click in an open area of the bin and PASTE (clip). Do this as many times as needed.
Then select one of the copies and in the preview window drag the red scrubber line to where you want to begin, and click SET START. Drag it to where you want to end and click SET END. Then use the ADD button (or click its chevron, for choices) to place the clip on the sequence or drag it there. Each copy can have different IN/OUT points.
Another method is to place an entire clip on the sequence, then split out the parts that aren't needed. If a clip is dragged from the timeline back to the bin, a copy is made and it vanishes from the timeline. But if <crtl-Z> (EDIT | UNDO) is then pressed, the clip returns to the timeline and the copy is retained in the bin.
