The answer is that it would be easy.
Discourse has a Theming system (see themes tag) that makes the kind of changes you’re talking about just a matter of adding the right CSS rules.
You can add CSS either directly in the “Site Customisations” Admin Panel UI, or on your local machine in your editor of choice via the CLI, with the ability to preview changes instantly on your site.
If you’re not a coder, you can hire one in the #marketplace.
As has already been mentioned, you can use my header search theme component for the header search part of your list.