1. How can we open search results in a new tab or window when clicking on the result?
2. Is there a way for each result to reveal those options when control-clicking on the search result (to open the OS options window)? That way, from the search list, I could select multiple results, one a time, opening them in their own tab.
This is essential for the research I do, having the ability to open multiple search results.
2. This is not possible, at least not without a decent amount of custom coding. The control-clicking alone is not enough, as there is an additional action needed to trigger the opening of the selected results, perhaps as a right click/open context menu. That is not an easy task to achieve and maintain, given there are many different browsers and devices (including mobile phones).
For customizations, I can recommend wpkraken, they have a dedicated team to work on orders, specifically on WordPress environments.