You can easily disable the Google search suggestions from Firefox, if your default search engine is google.You can also use this method to disable search Suggestions for other search engines.
Click the Firefox application menu icon and select Settings. Then click the “Search” from left sidebar and go to the Search Suggestions section. Then uncheck “Provide search suggestions”
Now go to the Privacy & Security menu from the left sidebar and uncheck “Remember search and form history” under the History section
And restart Firefox.
