That’s very dicey stuff. There are a lot of uncertainties about the composition of these bodies, from one to another, essentially boiling down to how solid, cohesive, and homogeneous they are. At the very high speeds and energy densities involved in a collision, a rather extreme form of fluid dynamics is in play. We DO understand quite a bit about those dynamics, given a known target material, but, if the material varies from asteroid to asteroid, and quite possibly laterally and with depth within an asteroid, unless a target point on the proposed “weapon” asteroid was carefully scrutinized (and at some depth), with some additional analysis of the rest of the body, smacking the asteroid into Earth within a few hundred miles of a given spot would be highly unlikely.
All this activity, plus the shove of the asteroid itself would have to somehow be kept secret / unobserved.
The uncertainties about the target body are part of why the results in this particular test had such a very wide range of possibilities. That can be narrowed down a bit, but overall the whole idea is pretty impractical with technology humans will have in any less than 100 years, at the rate we are going presently.
Yes, which is why they smack them with projectiles and analyze the debris cloud. If a body was found to have a solid enough composition they might attach large solid-fuel rockets to it and fire them off to get a deflection when the object was only weeks or days away from closest approach to Earth.
Once the change in course was detected the target area would have some warning but realistically how long would it take to evacuate a continent?