PHP
I have two Magento installations running versions 1.6.1.0 and 1.7.0.0. I am looking to upgrade my server to PHP 5.6 and Google wasn't particularly convincing that this is possible.
Can someone please confirm with certainty if 1.6.1.0 and 1.7.0.0 run properly under PHP 5.6?
The error you are getting from OpenSSL indicates that the SSL extension of PHP is compiled and loaded so no need to compile or load any .so or .dlls.
This is most likely a CA verfication issue - your SSL client (in this case PHP) is trying to verify the server's authenticity using root certificates; That's good - the only problem is this fails. Usually this means one of two things:
The server does not present a valid SSL certificate; This is unlikely for a well established email provider, I'm guessing you're using Google so this is probably not the issue.
More likely, your server does not have the up-to-date root certificates installed, or PHP does not know where they are. This is a configuration issue and solving it differs from server to server depending on your Linux distro and on how you installed PHP (e.g. from source, distro packages etc.). If you can provide more details about that, it may be possible to help.
Magento 1.7 does not support PHP 5.6
It says so on the official system requirements page
You can expect a Blank screen when you upgrade.
I advise you to test PHP 5.6 on a stage site first before going live.
Best Answer
Magento does not officially support 5.6 at any version, nevermind the older 1.6.x.
At present there are patches for 1.8 and 1.9 for PHP 5.5 support.
http://devdocs.magento.com/guides/m1x/system-requirements.html