Let's say two comets crashed into each other. If it was 0.1 AU away from the Earth, would the collision cause mass destruction here, or not affect us at all?
It depends. There are collisions amongst asteroids that have been caught on film that had no effect on us whatsoever. In your scenario, they would have to have a resultant vector towards us in order to cause any problems. Then there is the question of how many resultant particles are big enough to cause any problems (that is, big enough to get through our atmosphere and cause damage, see NOTE 1).
Keep in mind that space is big! The cosmic billiards you are proposing are about as likely as a K-T type event. Not at all likely. And our species is actually getting to the point where we may be able to do something about it. I highly suggest you read "Death From the Skies" by Dr. Phil Plait (an astronomer that has researched all this sort of stuff). And keep in mind that even 0.1 AU is still 14.9 MILLION kilometers!
NOTE 1: Many factors will play into even this. Such as the composition of the particles, their size, their trajectories, etc. For instance, the Tunguska Incident was caused by a piece of debris that is estimated in the tens of meters size. However, its composition yielded an air-burst. Whereas, the Arizona Crater from 50,000 years ago was caused by a mostly metallic impactor, which was also only 50 meters across. The main difference here is that because it was more metallic, it made it to the surface mostly intact. Since comets are mostly made of ice and loose rock, the threshold for larger size resulting in air-bursts would probably be higher. Again, read Dr. Plait's book.