How to setup advanced filtering options?

Hi!

I am sorry by advance if i post several questions in the same post, it seems that you don't really like it (i read a lot of posts in this forum before asking this), but they are closely related.

First, i know that what i want to achieve is not available in this extension as it is. It means that i don't really ask you for all-made solutions, but the extension is complex and i need clues to what could be done and locating the modules or files for that. I have enough knowledge for the customizations (or so i hope!).

So, the forum works great, but for the current project it lacks some features that will be mandatory. Mostly advanced filtering tools.

We'll have to be able to filter the post list with more than just status. Precisely, doing cross-filtering with tags/post-types/categories/status/priorities with possibility to select more than one. I can provide the UI elements for that, but what would you recommend to be easier to do?
_use the search query modified to trigger new pages for each selection set?
_customize modules / create a plugin to change the way the content is retreived
_add changes to the REST Api (knowing that it is not really in my knowledge)

Additionally, for the search queries, i see that there is already filters for multiple categories and tags, but they show up only after a first search. Is there a way to display them from the start?

I would be really glad for any help on this!
Thanks