Adding search to header

[Sustainable_Polymers]

Hello!

I am wondering how to add the search icon to my header (as in http://unicon.hellominti.com/#)
I do not want to add the shopping cart.

I have tried going into WooCommerce as I saw in a different help post, however the only option I have in WooCommerce is to activate the shopping cart (and if I do, only the shopping cart shows up).

Additionally, is it possible to add an icon to a menu item? We have a secure page in the menu that I would like to add the FA lock icon next to if possible

Thanks!

Ticket