I don't totally grasp what the problem is. First where are you searching from the google website it self? you punch in your search but then it forwards you to mozilla?

Are you placing the search in the main URL bar at the top? then it's sending you to mozilla? or are you using the smaller search bar at the top right, type in your search, then select like wikipedia, but then it sends you to mozilla?

Also what's the exact version you are using and your OS as Firefoxs is layed out completely different from these versions,..

I said:

    Formerly (before a reinstall) it would give me about 16
    characters of a blank line with a winking cursor in the
    address bar as a Bing search  bar. 

I meant: "in the url bar". (Is this standard usage?)

I am on any page. The unwanted Mozilla start pops up immediately when I hit the "search" key, highjacking the page I was on.

I am using FF 51. I don't want 52.