你姓什么?&您贵姓?—— People will just answer you their last name. e.g. 我姓张/免贵姓张
你叫什么(名字)?& 你的中文名字叫什么?—— People will answer their full name, not only first name.
请问怎么称呼?/应该如何称呼您?—— What should I call(address?) you? Formal and polite. Used a lot.
请问阁下是?—— Normally not used in real life, but in some literature. A little bit Shakespeare.
Generally, we don't ask people for their nick name. If they'd like to use nick name, they'll tell you so don't worry. But we do have a tendency to use something like 小张、老王, especially in working relationship. You can regard this as some kind of nick name. If the people around you use these a lot, feel free to use them, too. Also, if there are three characters in one's name, you can shorten it for the last two, or if there are only two character, save the last one and add 儿. These are normal cases in northern part of China, but I think most southerners prefer the whole name.
Sorry that there is only one line really answers your question. _(:з」∠)_