Hi 👋
Flarum uses the jsonapi.org response format. You can include models linked to the discussion model to the response with the include= URL parameter (if the model you need is properly set up).
If I am correct, it is currently not possible to search in discussion titles (the filter[title] parameter isn't available), so the filter[q]=keywords would be the parameter you can use to search in discussions.
For example, the following URL filters on keyword and only includes the firstPost and the tags. But when you remove the tags from the url, only the firstPost will be added to the result.
https://discuss.flarum.org/api/discussions?filter[q]=keyword&include=firstPost,tags
The url without tags included:
https://discuss.flarum.org/api/discussions?filter[q]=keyword&include=firstPost