Yes, it's rather strange. Characters exist within their own storylines, and abridged fanfiction is a meta - concept. They are not supposed to be aware of these fan - made interpretations. It's like they are stepping into a parallel universe where their stories are distorted in a condensed and sometimes comical way. It goes against the normal flow of their existence within the original narrative.
It might seem strange at first. Characters are used to their own established story arcs and personalities. When they watch abridged fanfiction, they are exposed to different takes on those. It's like looking at a fun - house mirror version of themselves. But on the other hand, in a fictional world where anything can happen, it could also be seen as an interesting exploration of how their stories can be reimagined in different and unexpected ways.
It can be. Since fanfiction is a creation by fans outside of the original canon, it's not something the characters would typically encounter in their own 'world'. So seeing an abridged and often altered version of their story would be quite a strange experience for them.