All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The scholars provided different views whether sequencing in washing the body parts in the Wudhoo' is obligatory or not. It is obligatory according to the Hanbali and Shaafi‘i scholars and recommended according to the Maaliki and Hanafi scholars. Shaykhul-Islam, Ibn Taymiyyah said: "The difference in opinions regarding the sequence of washing the body parts in the Wudhoo', as well as other acts of worship and contracts, is famous. According to Ash-Shaafi‘i and Ahmad, it is obligatory; according to Maalik and Abu Haneefah, it is not."
According to the opinion that sequencing is obligatory, then – by your action – you always left out wiping the head and washing the feet. In Al-Mughni, Ibn Qudaamah said: "If one washed his face, then wiped his head and then washed his hands and feet, then he has to wipe his head and wash his feet again."
Moreover, you did not mention blowing water out of the nose after sniffing it up; the majority of scholars are of the opinion that it is recommended, as stated by Al-Hafith Ibn Hajar in Fat-h Al-Bari.
Consequently, you should repeat all the prayers you performed during that period out of prudence in religion and in order to keep away from the relevant difference in opinions among the scholars. You should continue to repeat prayers until you mostly believe that you are no longer liable. Al-Hasan ibn ‘Ali narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said: "Leave what involves doubt for what involves certainty." [At-Tirmithi and An-Nasaa’i]
We advise you to learn about the Sharee'ah rulings, particularly the individual obligations, such as the five pillars of Islam. The Prophet, sallallaahu ‘alayhi wa sallam, said: "Allaah makes a person for whom He wants good knowledgeable in the religion." [Al-Bukhari and Muslim]
Allaah Knows best.