It sounds like you are installing and uninstalling plugins, rather than activating them and deactivating them. If the jetpack folder exists, then you are possibly trying to install it twice(?). If it's not showing on your installed pugins, however, then it looks like a previous uninstall failed.
Could you explain better what you mean when you say "When I did a search of the plugin-nothing comes up."
The vertical dots are coming from something with a class of "the_champ_sharing_container the_champ_horizontal_sharing", which is from the Super Socializer plugin, not the theme.