Hi there,
You can create a full-page front page with two buttons by using the header element:
https://docs.generatepress.com/article/header-element-overview/
However, both A & B requirements will require custom solutions which are out of the scope of this forum.
You could try looking for a pop-up window plugin and see if it satisfied the requirements.
If not you’d need to hire a developer to create the custom solution for you.
A site like https://codeable.io/ might be a good place to start 🙂