Is it obligatory to repeat ablution if one doubts its validity or its original existence, and is prostration of forgetfulness sufficient when in doubt about performing a rak'ah during prayer, or must it be repeated?

No attention should be paid to doubt that arises after completing an act of worship, such as ablution (wudu') or prayer (salat). However, if doubt arises during the act of worship, one must perform what was doubted and build upon certainty. If one doubts the original performance of ablution, they must perform it, because the default is non-existence.