1. Did you finish reading that, Harry Potter novel?
(What is the part of speech of 'that' in the sentence? Do we need "comma" after 'that'? Is the sentence correct?))
No comma needed.
The word "that" is usually a demonstrative pronoun.
http://grammar.ccc.commnet.edu/grammar/pronouns1.htm#demonstrative
In this sentence, it's serving as an adjective (see the second section and examples in the link above) modifying "Harry Potter novel"
To determine the part of speech of "that" in the sentence, we need to understand its function in the sentence. In this case, "that" is used as a pronoun, referring to a specific Harry Potter novel. It is acting as the direct object of the verb "reading."
As for the presence of a comma after "that," it depends on the intended meaning of the sentence. If the writer is referring to a specific Harry Potter novel, then a comma is not necessary. The sentence would be correct as: "Did you finish reading that Harry Potter novel?"
However, if the writer is using "that" as a relative pronoun to introduce a subordinate clause, then a comma is needed. For example: "Did you finish reading, that Harry Potter novel written by J.K. Rowling?"
In conclusion, whether a comma is required or not depends on the intended meaning of the sentence. The sentence can be correct with or without a comma after "that."