You can start by looking on fanfiction websites like Archive of Our Own (AO3). It has a large collection of fanfics from various fandoms, including ones for kyouka x atsushi. Just use the search function and type in the relevant tags.
Honestly, there's no definite answer on when the BSD manga will end. It all comes down to various factors like the author's inspiration, the popularity of the series, and the publisher's decisions.
Hard to say when it'll end. It could be influenced by various factors like the popularity of the series, the author's creative vision, and publishing decisions.