Is the prayer of one who doubts the number of rak'ahs, then completes his prayer and then performs the prostration of forgetfulness (sujud al-sahw) valid? And should he always add a rak'ah if he doubts the number of rak'ahs?

Whoever doubts the number of rak'ahs should base it on the lesser number, unless he is afflicted by obsessive whisperings (waswas), in which case he should disregard the whisperings. If it becomes clear to the worshipper that he added an extra rak'ah after basing his prayer on the lesser number, he must immediately sit for the tashahhud. If he continues with the extra rak'ah, knowing the ruling and doing so intentionally, his prayer becomes void. However, if he was ignorant of the ruling, his prayer is valid.