On your site I saw google search adding #gsc.tab=0 to the end of your url. 'Googling' this made clear that lots of people have issues with this at the moment - especially today! Now I don't know if this was what first caused your problems, but it could be a bug where Google changed something that makes older installations stop working... Especially the fact that it worked for a bit and then stopped again makes me think this could be the case...
Maybe Google is going to fix this soon, you could wait it out... But I guess your ex collegue gave you the newest search-engine code to add to the Page template. A <div> is just a bit of HTML that a webdeveloper can easily add to the page template. So basically you need someone with access to your files, who knows what he/she's doing and have them add a <div></div> section and add the code to it.
I don't know if a paid upgrade is really part of the solution... Anyway, that is the most I can tell you at this moment, I'm afraid...