Yeah tracking an ICBM towards an asteroid is extremely hard because of how fast the asteroid is moving and you would need a lot of explosive power to destroy an asteroid.

Depends on the size. Also, you can always predict where one will be if you track it. It's like sending probes to other planets. You send it in the direction the planet will be, you don't trail it. That being said, I'm sure a little bit of engineering and math could solve that problem.

Launching ICBMs would still be unreliable, yes, we could track an asteroid but whether or not an ICBM's targeting systems could track an asteroid is out of the question. ICBM targeting systems aren't meant for fast moving targets and missile tracking systems for moving targets are only exclusive to small and agile precision missiles such as the AIM-120D AMRAAM used on fighter jets, not an LGM-30 Minuteman III ICBM. It would still be more reliable to design a purpose built asteroid defense system, even with an improved targeting system for ICBMs we would still need a lot of planning if we were to destroy a missile with ICBMs, which wouldn't help if we get an asteroid headed towards Earth on extremely short notice, like that meteor which blew up over Russia which apparently nobody saw coming.