Is the fast of one whose throat was entered by water during ablution while he was fasting accepted, or of one who swallowed a hair during prayer, knowing that these matters may be due to waswasah (whispers/obsessive thoughts)?

Rinsing the mouth and sniffing water into the nose (istinshaq) should not be abandoned during ablution. A fasting person can perform them without exaggeration. The fast is not invalidated if water reaches the throat or a hair is swallowed unintentionally or due to an overwhelming urge. However, if done intentionally, it requires making up the fast (qada') along with incurring sin. Doubt does not invalidate the fast.