Cannot get notifications for incoming email or access email using skype

I am used to getting notification on incoming emails using my messenger tray icon. I also use the right click menu of the tray icon to access my email. I have tested installing skype on an older computer and these features are not there using skype. Is there a way I can still receive new email notifications and have a quick easy  access to email using skype or is this something messenger users will be losing out on when "upgrading"?