Only if you managed to leave the trajectory the same if it was already on a collision course or change the direction to a collision course. Do you think you can control that with a nuclear explosion? You probably don't know enough about to the system to make a high confidence prediction of the new outcome.
Not really, blowing it up is going to create a lot of fragments with slightly different orbits, and some are going to have practically the same as the whole Asteroid had before. So the chance of anything at all hitting earth will increase, but the parts will be smaller. It would be like a bullet turning into buckshot during flight.
If we were talking about a projectile fired at relatively close range on the surface of the Earth I would agree with you. But we are talking about a very small object very far away with already only a 1% chance of impact. Buckshotting the object with a random explosion is unlikely to change the dynamics of system to point where you say with high confidence the chance of impact is much higher. Some fragments might hit but it's very difficult to predict.
As long as some part of the asteroid keeps the old trajectory, the chance can only increase because you’re adding particles with slightly different trajectories.
Not necessarily. See my new comment above. In addition, depending on how far out you do it, gravity will allow it to reform. And if it never reforms because you blew it to dust headed out to interstellar space you wont get an impact either. It's not at all a simple problem.
