Avast has a feature that auto-checks the update status of a variety of software (browsers, plug-ins like Flash, etc), but the last "factory-issued" Flash Player update was back around 20 February. And Avast would hardly flag its own update message as "untrusted".
The symptoms you describe ("untrusted" prompt message, computer settings affected, occurring on highly-used site access like Google and YouTube) are those of either a computer virus or browser-specific malware. In that case, the update message could be a portal to try to get you to download and execute malicious code under the guise of a Flash update.
However, the timing you describe is possibly problematic: "Since updating to the new version of Opera...". When you updated to the new version, was there any period of normal usage of the new browser version before the onset of the Flash update message? If not, and if the problem began immediately upon updating, it's possible something was messed up with the Opera updating process.
OS: Win 7-64 SP1 -- Web Browsers: Opera 12.14u, 11.52; Firefox 27; Qupzilla 1.4.2; IE8