"I also bled the brakes using the brake pedal twice all the way around. Have I damaged the master cylinder? "
The risk is rust. Because you have a new (?) master cylinder, it hasn't had a chance yet to develop rust in the unused part. You'll know when you've damaged one in one of two ways; (1) the pedal will drop halfway, the failure light (if working) will light, and you'll lose braking to one of the rear wheels, and you won't be missing any fluid, or (2) the pedal will sink slowly while you keep pressure on it steadily at a stop light.
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Art Benstein near Baltimore
You spend the first two years of their life teaching them to walk and talk. Then you spend the next sixteen telling them to sit down and shut up.
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