Supreme Theme – Resize Map, Set Location-Page as Homepage and Filter for Search

1) I want to set the Location-Page as Main-Page. I tried to do this in Settings -> Reading. But the GD-Pages are greyed out here (in static page dropdown). Why are they greyed out? And how can I set it as Main-Page? (see attachment “homepage”)

Sorry, it is not possible to set the location page as the front page without a customization that falls outside support.

2) On the same page (Location), which I want to set as Main-Page, I also want to remove the textfield “Search for”. There should be just the address-textfield. I also want to resize the address-textfield (see the attachment “homepage”, where I colored the resize as green).
And I want to build a search filter on the same page. For this, I want to use the category bubbles below the textfields. Instead of using them as a search element, I want to add a checkbox on the top right of the bubbles (see attachment “homepage”, black rectangles on top right = checkbox). If the checkbox is chosen, the search should be filtered with the chosen category.

You can find custom CSS to hide search fields here: https://wpgeodirectory.com/docs-v2/faq/common-examples/#gd_search

GD Advanced Search addon includes the option to add a category select dropdown to the search bar.

https://wpgeodirectory.com/docs-v2/addons/advanced-search/

Im not sure, whether filtering with multiple categories is possible?
The permalink for restaurant is: “…/places/category/restaurants/”.
Is there a way for multiple category selection like this “…/places/category/restaurants+hotel/” or another way?

Not at this time, not without a customization

3)

On the listings-page, where the user can see the listings on the left and the map on the right, I want to size the map larger. The map should be sized at least 50% of the full width. (see attachment map) I didn´t find the place, where I can change the size of the map. Do I need custom css?

You will need to create your own custom CSS for that.
https://wpgeodirectory.com/docs/customizing-your-style/

4) And another question regarding the Membership. If I choose the 1 year membership, do I get after one year also access to all addons and themes? Or do I have to renew the membership to use them?

A license entitles you to addon updates and premium support while the license is active.