The best book that is available on Karanas is a book by Dr Padma Subramanyam. She has researched and reconstructed the karanas. It is in three volumes and it is called "Karanas"
Nattuvangam can be started after having a basic understanding of Tala. Some of the essential elements of rhythm are covered in the online program with respect to the logic of breaking down a korwe and how polyrhythmic structures are used in Bharatanatyam choreography.
To progress with nattuvangam, you must go to a teacher. This is personal preference and you can start whenever you feel you are ready.