How does Vesatility interact with
Toolbox? Would it effectively double the impact of Versatility, since each battle icon colour you flip is a separate instance, or does it just add 1 to the total being repaired?
[Source: Aequitas] 
Toolbox only adds 1 to the total being repaired. The 'for each' in Versatility is looping to calculate the amount of repair that will be done, then the repair is applied as one event.
Raider Ratbat works the same way.
Wave 1's
Chop Shop however works the other way. It has the repair inside the for each, allowing Toolbox to apply for each repaired damage.
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