<Crl-C> will copy a selection. <Ctrl-V> will paste it into the timeline.
If what you're attempting is to precisely line up to a split, use the icon under the preview window that positions the red line at the nearest split.
To mute a section, first right-click and UNLINK from video. Then split out the portion to be muted and delete it, leaving a gap. Or drag the newly split clip to another audio track and mute that track.