Yes, 'so much' can certainly be the subject of a sentence, and the sentence you've quoted is a common and natural example. Your understanding of it is correct: it means 'so many things have happened to us so fast'. In this context, 'so much' is better than 'so many things'. If you say 'things', it makes us think of a number of separate events. 'So much' is broader: it suggests the cumulative effect of these events, including less tangible experiences, such as emotions you have felt and changes that have occurred.

Yes, that is correct; both “much” and “many” can be used in that way as pronouns, and “so much” and “so many” can as well.