I installed the GMail app onto my Ubuntu 15.04 machine.
Upon logging in, a warning message appears, saying This version of Safari is no longer supported. Please upgrade to a supported browser
I then received an email from Google saying that my GMail account had been accessed from Safari running on an unknown OS.
Safari? Unknown OS? What's the reason for this?
I'm presuming that it's an issue with the user agent data set by browsers is missing or incorrect in the GMail app, which leads me to my second question - the Ubuntu "apps" are clearly just slimmed down web browsers, but which browser are they based on?
This is a bug and is being investigated - see the bug report on Launchpad
You receive that notification for security reasons.
Google always sends these mails, when your account is accessed with a new client software.
Probably GMail application sends incorrect information about itself. If it works OK, then there is nothing to worry about.
You can also find GMail maintainer and report this bug.