Yes you are right about the fact that I confused auto complete and search suggestions. So I just disabled search suggestions and all is good on that front.
About the plugin fix, I'm sorry but I can't see the file you uploaded… there is a message saying :
You can't view files in this topic.
Lastly, I would really like to disable front-end search settings but like I said, no matter what I do in the back-end, the front-end icon and drop-down are still always there. Do you know what can be done to fix this?
Thank you for your great support.