Learn Russian: Этот дом пустует, это жуткое место. - This house stands empty, this is an eerie place.

Пустовать is a specific verb meaning "to stand empty" or "to be vacant." While you could simply say Этот дом пустой (This house is empty), using the verb пустует emphasizes the ongoing state of the building remaining unoccupied over time.

Does жуткое always mean "eerie" or "creepy"?

In this specific context, yes, жуткий means "creepy" or "eerie" (derived from the noun жуть, meaning horror or fright). However, you will frequently hear it used in everyday Russian as an intensifier meaning "terrible" or "extreme," such as жуткий холод (terrible cold) or жутко интересно (terribly interesting).

In the phrase это жуткое место, is the word это in the neuter form to agree with the neuter noun место?

It happens to match, but no. Это functions here as the invariable demonstrative pronoun meaning "this is" (or "it is"). If the noun were masculine, such as лес (forest), the pronoun would stay exactly the same: это жуткий лес (this is a creepy forest).

The sentence joins two complete thoughts with just a comma. Is this punctuation correct in Russian?

Yes, it is perfectly correct. While English grammar strict rules consider this a "comma splice" and require a semicolon or a conjunction, Russian punctuation is much more flexible. Joining two closely related, short independent clauses with a simple comma is standard practice.