I was reading about Skyrim's background and it seems like many are assuming that the events in the two novels (the Infernal City and Lord of Souls) are actually part of the game's story. Is this true? I loved the books, but I really don't think that the stories fit well. Would this mean that Morrowind is now conquered and Vvardenfell is now destroyed?

I believe they are.

Yeah, they are.

Yeah, it's been confirmed they are.

remember OP, that these events take place 40 years after the oblivion crisis, where as skyrim takes place 200 years after, so 160 years have passed since the events in the books. Is vvardenfell still destroyed? yes, but morrowind might not still be conquered, orsinium could be rebuilt and who knows what else could go on in 160 years if so much could happen in 40.