Re the taskbar icon - it sounds as if you need to search for "notifications" in control panel, and in the result page set the Kaspersky icon to "Show Icon and Notifications".
As Aura says, only Kaspersky 2016 or the very latest latest version of 2015 works with windows 10. Multiple issues apparently exist.
The only one that has personally impacted me so far (running KIS 2016) is that newly pinned tiles to not appear ion the start panel until you log out, reboot, or restart the Windows Explorer process. Likewise unpinned icons to not disappear until one of those same actions is performed. This bug has been acknowledged as such by Kaspersky support, and a fix is being worked on (ETA unknown but knowing Kaspersky support, it could drag on a .... little...)
Edit :the pinning bug also seems to stop newly installed programs appearing in the "All Apps" list..And if you find that kaspersky really is not there - you wilt need to install the 2016 version - you probably will not be able to run a 2015 installer.
Edited by x64, 07 August 2015 - 03:57 PM.