I'm running Flash ver. 220.127.116.11 on a MacBook Pro with OS X El Capitan, ver 10.11.06. After trying to update FlashPlayer and being told I have a later ver already installed, I found that some things had changed. (1) Safari's home page was changed drastically. (2) The dots below the open apps in the Dock no longer appear, so I can no longer swipe between open full screen windows, and don't know what apps are open. What happened and how can I get things back to the normal we like!? To whom or what or where can I file a formal complaint?
Installing Flash Player would not change your dock behavior or the Safari home page.
Unfortunately, because Flash Player is ubiquitous, it's a popular target for impersonation by malware authors. It's incredibly difficult to install software without the user's permission, so malware authors tend to focus on the weak link, which is now the human factor. I'm a little concerned that you were tricked into downloading something that wasn't actually our installer.
I'm also very curious about what your Safari looks like now. A screenshot would be very informative.