Inserting icons & search bar on top of header image

Hello there,
I have looked for this info in the “Highwind theme” support already with no help there so I thought I’d ask here. This is what I want to do:

1. Add a horizontal row of social media icons to the right side of the header so they appear on top of the image.

2. Add a search bar right underneath the row of icons also to appear right on top of the image.

The business I am designing this website for wants it to look exactly like the header on this website: https://https://www.seibertron.com (Obviously with a search bar underneath the icons instead of the links.)

Here is the link to my website: https://www.toyfevertoys.com

I also realize that I may have to make the header space bigger to fit everything in so any help I could get would be greatly appreciated! Thanks in advance!