What happens if two effects are trying to modify the damage a character takes?
In cases like that, the player whose character it is can choose which effect to apply. Then see if the other effect(s) still apply. Keep applying these effects until none apply. Each effect can apply to the same damage only once.
When my opponent plays Decepticon Shockwave
and plays System Reboot
s to make me discard, say, 10 cards, if I have a Defensive Driving card attached to one of my characters, can I choose all 10 damage to be dealt to that character and make it all to zero since Shockwave ability reads as deal 1 damage to it?
Yes, Shockwave’s ability triggers individually per card discarded, so each instance of 1 damage would be reduced to 0 because of Defensive Driving.
Say for instance that you were playing a full team of Aerialbots, with four planes in vehicle mode. Your opponent played a Strafing Run
last turn and spread one damage to each of your characters. Your opponent has a Defensive Driving attached to one of their characters. You play a Bombing Run
to move one damage from each of your planes to that character. What happens? Is all damage from Bombing Run dealt with a single damage at a time, per plane you have, or is the damage tallied and then moved in a single chunk? In other words, does that character take three damage from Bombing Run thanks to Defensive Driving, or none at all? Does Defensive Driving block Bombing Run at all, or is "moving" the same as "taking damage"?
Moving damage counters does not count as repairing or taking damage. So Defensive Driving would not block damage in this scenario. Maybe take a look at Bumpers
Defensive Driving makes reference to an opponent's "cards". What constitutes a player's cards in this case? Does this include abilities from bots on the field, in addition to played upgrade and action cards?
Every card. All of the cards.
Yes, each damage is individual and not a lump sum so it will be reduced to zero.
The abilities would cancel each other out, and just do the printed damage from the effect of the character or battlecard.