What really messes up flow is traffic "waves"[1] and these are often caused by drivers hitting the brakes because they're following too closely or someone cuts in front of them aggressively.
Yep - follow distance makes a huge difference in both safety and traffic flow. If you can leave 20 cars in front of you, do it. You get there just as fast but have more time to react and don't need to hit your brakes as often.
Yes. Once I realized this, I tried to put a higher priority on maintaining a more steady average speed, even though that usually means leaving a larger gap ahead of me.
Of course, the problem then becomes that people will often use that gap to cut in front of you, thus negating much of the benefit. Tragedy of the commons.