Does the incorrect ablution with which the Hajj and Umrah were performed affect the validity of these rituals and his marriage, and what is the opinion of the Hanafis regarding the described method of ablution?

We hope the questioner's Hajj and Umrah are valid and rewarded.

The correct view is that washing the hands at the beginning of ablution is not sufficient for washing them up to the elbows, because it is either done with the intention of a sunnah (recommended act), in which case the intention was missed, or with the intention of an obligatory act, in which case the sequence was missed.

As for the Hanafi school of thought, it holds that washing the hands at the beginning of ablution is sufficient, whether with the intention of an obligatory act or not. Some of them have chosen that it is an obligation and its performance first is a sunnah; others, that it is a sunnah that substitutes for the obligatory act; and a third group, that it is a sunnah that does not substitute for the obligatory act.

Ibn Abidin clarified that there is no contradiction between these views, as the obligatory act is implicitly fulfilled, but reward is only achieved with intention. Therefore, it is recommended to rewash the hands when washing the forearms to intentionally obtain the reward of the obligatory act.

Based on the Hanafi school of thought, your previous purification was valid. Even if this view is less preferred by us, adopting a less preferred view after the event has occurred is permissible according to many scholars. Therefore, you are not required to repeat past prayers.

As for your Hajj, we hope it is valid, because Sheikh al-Islam Ibn Taymiyyah believes that purity for tawaf is desirable, not obligatory. Some scholars believe it is obligatory and can be compensated for by an animal sacrifice (dam), which is what you did, so there is no blame on you. However, if one adheres to the view that purity is invalid and a condition for the validity of tawaf, then your Hajj is not complete, and the tawaf al-ifadah and sa'i remain due. If you performed Umrah after that, then the tawaf and sa'i of your Umrah suffice for your Hajj.

And Allah knows best.