Hi David,

OS X 10.6.8 and Safari 5.1.10 are the last versions available.
Snow Leopard is no longer supported. It is an outdated OS and won't be updated 
again. 
Unless you upgrade to a newer OS X you will continue to have problems using 
Safari no matter which version of Safari you have installed.

For your Flash Player issue:
1. Completely uninstall and reinstall Flash Player.
Uninstall Flash Player | Mac OS
<http://helpx.adobe.com/flash-player/kb/uninstall-flash-player-mac-os.html>

2 Then download and run the installer again.
http://fpdownload.macromedia.com/pub/flashplayer/current/support/install_flash_player_osx.
 dmg

For your Gmail security issue, the only thing I can suggest is use Google's 
Safe Browsing for Firefox browser
<http://www.google.com/tools/firefox/safebrowsing/>

Cheers,
Ronni
> On 14 Dec 2014, at 11:25 pm, David Noel <[email protected]> wrote:
> 
> -- 1. Using Safari, I find that trying to open a page which has Flash
> content gives:
> 
> "Adobe Flash Player" is out of date.
> The version of "Adobe Flash Player" on your system does not contain
> the latest security updates and has been blocked. To continue using
> "Adobe Flash Player", download an updated version from Adobe's
> website.
> 
> -- However, if I click on "Download Flash..." and apparently do the
> installation, the same message comes up with Safari, even after
> closing and opening Safari. What can I do? If I open the same page
> with Firefox, it works OK.
> 
> -- 2. If I open my gmail account with Safari, it opens and works OK,
> but has a banner at the top:
> 
> This version of Safari is no longer supported. Please upgrade to a
> supported browser. Dismiss.
> 
> -- I'm using OS X 10.6.8 and Safari 5.1.10. Safari doesn't seem to
> have a "Check for updates" command. Any advice, please?
> 
> David Noel
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