Well, it should be pretty clear that the purpose of putting buttons (or whatever you want to call them) on a lower pants leg is to make it easier to put on and remove tall boots.
In turn, tall boots as a garment are much more useful in an era of horse-borne travel and unpaved roads. If you don't make that connection, perhaps the riding crop there in the picture might clue you in.
I can't say most. I'm not sure where hard numbers for this would come from (if someone finds them, they can count on an upvote from me). But it certainly seems fair to say that this would be much more common attire in the 1800's than today. On the other hand, sitting for a painting was a fairly laborious process, so any person you see in one is almost certainly going to be wearing some of their best (most stylish and expensive) clothes.