Remove searchbox from header and shadow round wrapper

This can all be achieved using CSS.

Try using a browser developer tool for this kind of exploratory CSS work.
I use Google Chrome’s built-in Developer Tool and it’s really easy to expose the webpage’s underlying HTML and CSS.

Now that you know the style, from being exposed by the Developer Tool, you can add a new style to override it.

You ought to add new styles externally, not within the theme’s files. Changes to the theme’s files will compromise the theme and be compromised when the theme updates.

External changes can be made using a Child Theme or through a plugin that provides Custom CSS functionality.

I recommend using the Jetpack plugin and its Custom CSS functionality to hold your CSS modifications.

To remove search from the header, follow this post

https://www.mouseclick.com/tutorials-2/adjust-header-image/

Which tells you to put the following code in your css. I put it in
Appearance>Theme Options>Layout>Custom CSS, but I think the author wanted in the style.css.

This is what it says to do…

Add the following lines to your CSS section:

#header input#s {
display: none;
}