What is incumbent upon one who swore many oaths in the past, of all kinds, and does not remember their number, and has repented from that; is expiation obligatory upon him, and if so, how many expiations?

One should not frequently swear by Allah, and you have done well by repenting to Allah. Expiation is obligatory for every oath you have broken. If the oaths were multiple but pertained to a single matter, then one expiation suffices. However, if they pertained to different matters, then each oath requires a separate expiation. If you do not know the number of oaths you have broken, then act according to what you predominantly believe to be true and take precautions regarding expiation. The "Ghamus" oath (a false oath sworn deliberately to deceive) is not expiated except by sincere repentance. Some scholars hold that expiation is also required for it, along with repentance, and this is the more cautious approach.