What is the ruling on forgetting a condition or a pillar of ablution or being ignorant of it, and then praying with that ablution, or forgetting a pillar of prayer or being ignorant of it, regardless of whether the time has expired or not?

As for what falls under the category of committing a prohibited act, ignorance and forgetfulness are excused therein. Such an act does not invalidate the worship, nor does it necessitate an expiation, unless it falls under the category of guaranteeing damages, like hunting game during the state of ihram (definition). However, as for what falls under the category of performing a commanded act, the ignorant and the forgetful are excused from sin, but if they have not performed the commanded act correctly, they must perform it, because their responsibility is occupied by it. Examples of this include: one who omits an obligatory part of ablution or a pillar of prayer.