ICBMs are a lot faster than that.
On their way up, yes.
As far as I know, the warhead is in free fall on the way down, and it decelerates very quickly after launch phase and once it strikes the atmosphere.
I would be really surprised to learn that it detonates at faster than 1,500 mph.
Anyway, I spent 10 minutes on Google and came up with lots of information on launch speed and reentry speed, but nothing on impact speed.
I saw several “terminal velocity” numbers, but those look exactly like the reentry speeds, so I'm dubious.