How would you gauge my success?
Being an honest and sincere employee, it is your right to know what you can do to achieve professional success. You should ask your boss that how he or she would assess your performance after 3, 6 or 12 months. By knowing your objectives, it would be a lot easier for you to claim promotions or bonuses.
How would you like to be communicated?
Communicating to your boss on day to day basis is imperative. However, you should clearly ask your boss about the medium of communication as well as the time he or she would prefer. Some people like to be communicated only through official means of communication; whereas, others give some flexibility to their subordinates.
Many bosses often have a problem about the frequency of communication as well; therefore, it is highly recommended that you make such things clear beforehand.
What areas do I need to improve in?
This question is going to leave a very good impression on your boss as he/she would think that you are keen to get rid of your flaws and want to become a more productive employee of your company. Ask your boss specifically about the areas you need to improve in.
What are my strengths?
If you wish to know about your strengths, you should find a right opportunity to ask this to your boss because he or she is likely to be the best judge of your abilities.
Am I missing anything?
Having taken a briefing from your boss about any topic, you should take a minute to go through all the important details and then ask your boss if you are missing anything or not. This will save you from embarrassment in future.