The book was written concurrently with the movie. See the book "The Lost Worlds of 2001" for various versions of it.

https://www.amazon.com/Lost-World-2001-Arthur-Clarke/dp/0451...

I listened to a podcast about it ages ago, and if my memory serves me correctly - the book was started first but wasn't finished until after the movie had been completed. Kubrick couldn't wait for Clarke to finish the book, so he carried on with the production of the movie. I think Clarke wanted to release the book first, but Kubrick wasn't going to wait for him!

No. It was developed concurrently with the film version and parts of it were even based on Clarke's earlier short stories (e.g. The Sentinel).