The examples you gave are all grammatically correct, but they are slightly different in meaning.
Beijing zai nār/nali?
This sentence is asking where is Beijing, the person who will be answering the question will tell you the location of Beijing. If I were to answer the question, I will tell you Beijing is physically in Hebei province, in the east part of China.
Beijing zai na guo?
This question is asking which country is Beijing in, and will be answered by justing telling you Beijing is in China.
Beijing shi nar/nali?
This is a little different with the previous two, it is not only, or, exactly asking the physical location of Beijing, it is asking about Beijing itself. I will answer as the following, Beijing is the captical city of China, its population is 13 millon and it is in the east part of China and so on.