wim_mutsaers please describe your use case in more details and what you have already tried. Also please describe the skills you possess or have access to, as advanced customization requires writing custom code.
The best solution for minimal complexity and ease of long-term maintenance is to use only extensions, then perform cosmetic changes using custom CSS. This way the changes will stay and/or are easily reversible when you update Flarum and your extensions in the future.
For advanced theming, Flarum is a single page app written with Mithril. To modify the behavior of the header and navigation, you will need to extend or modify the Mithril components. Whenever possible, you should try to re-order elements with CSS flex as it will be easier than maintaining modified Mithril components.
There are a few existing Flarum themes in the extensions that you could take a look at.
If by dropdown menus you mean like the menu we have on the header here, it's the FoF Links extension https://discuss.flarum.org/d/18335-friendsofflarum-links You could then use custom CSS to modify the look if you need.
If you have a main website generated using a different framework and are trying to unify the header between all the platforms, it's definitely possible and some big websites have done it, but it requires some good knowledge of all softwares involved.
If you want to put something completely static (HTML) above or below the single page app, it can be done using either the built-in fields in the admin panel or the PHP content extenders. But you will likely need some custom CSS to make the app play nice with it. The additional space taken by the custom HTML might interfere with the column and mobile layouts of Flarum.
