Was there any crossover between them? Did they use a little of both at some point? Do they do that now?

Most animation is still drawn frame by frame. Episodes get worked out and storyboarded by the production team, and then it gets sent (usually) to South Korea for frame-by-frame animation by hand.

Most editing is done digitally now, with some scenes digitally animated (you see this a lot in Futurama, and occasionally the Family Guy). But the animation itself is done by hand in South Korea.

In terms of things looking jerky, that's just a budget and style choice. 24 fps is pretty standard, so if you go below that, things look choppy.