I’m sorry there’s something wrong with the plugin. If it was really faulty, deactivating it was the right choice.
I must admit I don’t really understand what happens. Do you know which addresses are causing the 404? Normally you should get messages such as “The URL https://example.com/favicon.ico
is not accessible”, so you know what’s wrong. I also don’t understand the procedure (“the favicon is the icon we download from my website to my fav bar”): what did you do exactly?
If your site is online, could you give me its address to I can do a quick review of your code?