i just installed opera on a vm with LEAP42.1 and I don’t encounter any issues. I downloaded the rpm from their site and installed with zypper install. It complained that there is no key with the rpm but I chose to ignore that for now(is just for this test) and i was able to browse with Opera.
There were some other issues with it few weeks ago(in another thread about Chrome(but i encountered also with Opera at the same time in 13.2)) but the errors were not as the ones you are encountering now.
More details would be needed to see what is wrong on your system. What repository did you install it from?
Would you try to uninstall and than install it manually with zypper?
Which version you have? I installed opera-stable_35.0.2066.82_amd64.rpm
rpm -qi opera
Name : opera
Version : 32.0.1948.69
Release : 1.1
Install Date: Wed 24 Feb 2016 04:25:27 PM CET
Group : Productivity/Networking/Web/Browsers
Size : 154793870
License : SUSE-NonFree
Signature : RSA/SHA256, Fri 23 Oct 2015 08:03:59 AM CEST, Key ID b88b2fd43dbdc284
Source RPM : opera-32.0.1948.69-1.1.src.rpm
Build Date : Fri 23 Oct 2015 07:53:35 AM CEST
Build Host : build11
Relocations : (not relocatable)
Packager : http://bugs.opensuse.org
Vendor : openSUSE
URL : https://opera.com/
Summary : Proprietary web browser
Opera is a proprietary, fast, and user-friendly web browser.
It includes web developer tools, news aggregation, and the ability
to compress data via Opera Turbo on congested networks.
Distribution: openSUSE Leap 42.1
System always updated.
In my case problem exists only with Google.
Other websites via https:// work fine.
So I guess… it’s certificate?