What is the ruling concerning the past prayers and ‘Umrahs performed by the questioner with an ablution in which he did not wash his hands due to his ignorance?

If you did not know that washing the hands up to the elbows is one of the obligatory acts of ablution (wudu'), and you used to wash your palms with the intention of obligation, then your ablution is valid according to the Hanafis and Malikis. As for schools other than the Hanafis, if you used to wash your hands with the intention of it being a Sunnah, and you did not wash them up to the elbows, then your ablution is incomplete, and you must make up the missed prayers. The making up should be done according to one's ability.

Some scholars are of the opinion that whoever neglected this out of ignorance only needs to repeat the prayer of that specific time.

As for circumambulating (Tawaf) while you were not in a state of complete ablution, it is invalid according to the majority of scholars. You must go to Mecca to repeat the Tawaf, Sa'i, and perform the halq/taqsir (shaving/shortening the hair).

However, if you adopt the view of those who do not stipulate purity for Tawaf, then your Umrah is valid, and you owe a dam (sacrificial offering) for each Umrah due to neglecting the obligation of purity.

It is permissible to adopt a less preferred opinion after the matter has occurred, so you are not obliged to repeat past prayers, and your circumambulation (Tawaf) is valid. A Muslim must strive to understand the affairs of his religion.