Does ablution become invalid if one first washes the hands, then rinses the mouth and nose, then washes the face, then wipes the head and ears, then washes the hands up to the elbows, and finally washes the feet?

The order of actions in ablution (wudu') is a point of contention among scholars. The Shafi'i and Hanbali schools hold it to be obligatory, while the Maliki and Hanafi schools consider it not obligatory. Accordingly, based on the opinion of those who deem order obligatory, you were omitting wiping the head and washing the feet, as mentioned by Ibn Qudamah in Al-Mughni. Furthermore, you did not mention istinthar (expelling water from the nose), which the majority of scholars consider to be recommended.

Therefore, out of piety and precaution, you must repeat all the prayers you performed with the aforementioned ablution and continue to make up for them until you are reasonably certain that you have fulfilled your obligation, in accordance with the Prophet's (peace and blessings of Allah be upon him) saying: "Leave that which makes you doubt for that which does not make you doubt."

It is also advisable to gain a deep understanding of religious matters, especially individual obligations (fara'id al-'ayn), as the Prophet (peace and blessings of Allah be upon him) said: "When Allah wills good for a person, He grants him understanding in religion."