The bar graph below show the TV viewing habits of Koreans.
What is the part of speech of 'below'? Is 'which is' omitted before 'below'?
The word "below" can be either an adverb or a preposition.
http://www.answers.com/below
http://www.bartleby.com/61/3/B0180300.html
http://www.m-w.com/dictionary/below
In this sentence, it's an adverb. It's telling WHERE something is.
You could rephrase the sentence to include "which is" where you indicated, but it's not necessary.
=)
The word "below" in your sentence is functioning as an adverb, modifying the verb "show." It is describing where the bar graph is located.
Regarding your second question, the phrase "which is" is not explicitly stated before "below" in this sentence. However, it is often understood or implied. In other words, the full sentence could be rephrased as "The bar graph, which is below, shows the TV viewing habits of Koreans."