2. Yes, in order for this to work, AG will need to access response body.
3. Yes, and in this case we'll need to use JS-based filtering (so-called extended CSS rules or scriptlets).
And here's an answer to the question you didn't ask: yes, this would be slower than doing the same with a browser extension. To make it faster, a different approach to filter rules is required - fewer generic cosmetic rules, more HTML filtering and removing elements from the page content.
The end goal is to completely get rid of any app or extension. Ideally, I'd like to see all the filtering moved to a server-side application like AdGuard Home.