JSON information for custom post types

I need to get information about posts from my web page that are custom post type.

In addition I use a list of categories and taxonomies to filter the posts.

Let’s say I have a custom post type named: “cars”
I have a list of categories like this: “bmw”, “mercedes”, “citroen”, “volkswagen”…
I have a list of taxonomies like this: “gasoline”, “diesel”, “white”, “black”, “red”…

How can I get the information about the posts that:

– belong to the “cars” post type and have the categories “bmw” and “mercedes” and the taxonomies of “gasoline” and “white”.

– the same as before but instead of “and” we put “or”.

Thanks for the help but I haven’t been able to figure out how to do that.