Is expiation due from one who fasted and was required to perform a purificatory bath (ghusl) from major ritual impurity (janabah), but was ignorant of the correct method of performing ghusl, and learned of this after the end of Ramadan? And is it obligatory to fast the previous Ramadans consecutively?

There is no need to make up for fasts if the reason for making them up was an error in ghusl (ritual bathing), as your fasting is valid under the circumstances you mentioned. As for the validity of your prayers while knowingly omitting one of the obligatory acts of ghusl, there is a difference of opinion due to your ignorance of the ruling. It is feared that you may be suffering from obsessive doubts (waswas), so abandon these doubts and do not pay them any attention. You can clarify the nature of the error in your ghusl so that we can explain what is required of you.