In Opera you can select some text and right click and select "Search with" to search the text with a search engine. Is it possible to configure it to open search results in a new tab?
Yes, you can modify the entry in the menu text file. However, you might want to try just holding down the shift key. This actually works for all menu commands and will open it in a new windows, just like if you shift+clicked a link in a web page.
The following links may be useful for you:
No, the search menu part
internal search with can't be edited.
You can edit most of operas layout - but not that.
The internal menus are generated by Opera and so cannot be edited.
However, you can replace the search menu with your own as explained in the source above.
But have in mind, that way, all newly created search engines aren't included in your modified search context menu.