Hello there,

The best way would be adding simple CSS code. You should navigate to Appearance > Customize > Additional CSS and add code below (don’t forget to change 20px to your desired size):

.navbar .navbar-nav li a{
font-size:20px;
}

I’m not sure if I understood well, but the easiest way to add search box into menu would be using one of the plugins. This one is very simply and works well:
https://wordpress.org/plugins/add-search-to-menu/

Thanks,
Piotr Bąk