Please have a look at DuckDuckGo if mainly privacy is of your concern. It will enhance your current searching experience greatly. I have had a quick look at Ixquick, and I do not see any reason why one would want to use an unknown copycat website that does nothing but worsen your searching experience compared to the great alternatives out there.
All of the major search engines seem to be included with Opera. Although the ability to set a custom search engine as default is currently missing, I do not see any reason for this to be an issue unless it is for a big player such as Baidu.
According to one of the posts that I have come across, Opera has disabled or removed this functionality due to safety concerns. Please keep this in mind, since it seems unlikely for this to change anytime soon.

I disagree and that's why I no longer use Opera as I have switched back to a Chromium based browser which allows me to use Ixquick as my search engine. If you are looking for safety you would eliminate Google as a search engine choice. Duck Duck Go is a horrible search engine. Ixquick...the best.

All of the major search engines seem to be included with Opera. Although the ability to set a custom search engine as default is currently missing, I do not see any reason for this to be an issue unless it is for a big player such as Baidu.

According to one of the posts that I have come across, Opera has disabled or removed this functionality due to safety concerns. Please keep this in mind, since it seems unlikely for this to change anytime soon.

You can add custom search engines, you just can't set them as default one.

I understand that...but that is very inconvenient which is one of the reasons I have switched to another chromium-based browser which allows me to customize my browser in the manner in which I am accustomed.