How to output html on a custom location with a wordpress plugin?

How can I use a self-made WordPress plugin to output for example a custom menu or custom HTML to a specific location? The only places I managed to output content is in wp_head and wp_footer, but is it possible to get content to show up anywhere else? Is it even possible to force the plugin to output the HTML for example inside a specific div or a DOM element?

Example scenarios

1. I want to add a custom button that triggers a menu or modal, but the button needs to be located inside the header and I also need a place for the modal HTML before the footer (example).

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2. I want to add custom made “social share buttons” to every page and need a place to output the HTML after the page title.

Just to give you a feeling of what I’m trying to do…

Maybe I’m just way off track. I am new to this, but I am eager to learn.

“Teach me the ways of the force”

Appreciate any help, Thanks 🙂