Placing Search Icon in the Header Menu

Hello,

Questions have been asked on this forum about moving the Search function to the Header Menu.

However, I would like to use a Magnifying Glass icon for the search in the menu – it takes up less space on the menu. How would I accomplish this?

Finally, is there a way to center the menu across the screen?

My site can be viewed at https://gravelcyclist.com

Thanks in advance for the help!