How valid is it to repeat fasting the make-up days from Ramadan when in doubt about swallowing saliva or ritual purity, and is it obligatory to make up every day about which doubt arises?

Fasting is not broken by swallowing saliva, nor is purity a condition for the validity of fasting. Therefore, the claim that one must make up for fasts due to swallowing saliva or lack of purity is incorrect.

The questioner is afflicted with waswasah (whispers/obsessive thoughts), and the cure for it is to ignore them.