Is it permissible for one afflicted by waswas (obsessive whispering) to hasten in prayer, or to say words like "Islam" when reciting "Guide us to the straight path," or to recite the tashahhud after every waswasa, in order to ward off satanic whispers?

It is not permissible to rush in prayer in a way that compromises the pillar of tranquility (طمأنينة), even if the worshiper is afflicted by obsessive thoughts (وسوسة).

However, there is no harm in a speed that does not compromise tranquility, with the intention of completing the prayer with devotion before obsessive thoughts attack. Al-Zubayr said, "We hasten [to finish] before the whisperings [of the devil]."

It is not permissible to utter what was mentioned in the question, nor to recite the Tashahhud after experiencing obsessive thoughts. These matters do not repel obsessive thoughts. Rather, obsessive thoughts are repelled by ignoring them and by occupying the mind with contemplating what the worshiper is saying in their prayer.