1. Is it polite to ask people question in this short form even in an informal situation?
Actually, these questions aren't too polite even in informal situations (e.g., with friends). This short question is more a form that a parent, teacher or other person in authority might use with those in a lesser position. It is quite insistent and demanding in tone.
2. What should be the right answers to each of these questions?
The same as for any question, e.g., “Yes, I do.” or “Yes, I understand.” Note that we sometimes use the “Understand?” => “Understood.” sequence (say by an army officer reprimanding a new recruit), but it is more like movie talk than normal polite conversation.
3. What should be the polite way of asking people whether they understand something taught? particularly when you are asking your boss or someone senior.
a. Do you get it? =Quite informal, not so good when talking to some one in a higher position
b. Have you got it? =Quite informal, not so good when talking to some one in a higher position,
c. Do you understand it? =MOST polite.
