Mental calmness during timed test taking
I would suggest getting used to self-proctoring practice exams within a certain time limit. Keep at it until you figure out how to determine when it is fruitful to skip a question. Come back to it later when you have an ah-ha moment or finish the exam. As for worrying about spending too much time or self-depreciating yourself, try to minimize it. Remember your successes. Take time to build up your confidence both inside and outside academia and strive to do the best you can do.

Think of every difficulty as a chance to be humbled, and use that outlook to find wisdom in the experience. In grad school, I'm sure you'll encounter this same feeling just by speaking with people whom are your senior.