Problem solved. Now, Opera in Google Search is opening mentioned sites/links/webpages. Haven't done anything. Obviously it has been some kind of a bug in Google-Opera.

It is weird. As mentioned above:
e.g. Wikipedia pages can't be opened when I am in google search (it redirects me to "intent://en.m.wikipedia.org/wiki/" and shows that the webpage is not available). But, if I sign in to my google account, then the same page opens. Also it opens in a new tab or in Bing. Problems also with lot of other sites/links. Anyone?

Confirmed. In Chrome it doesn't happen.