Which sentence is punctuated correctly? my father loved talking about history, particularly: the civil war, the cold war, and the revolutionary war. there were several scientific processes i wanted to learn about such as, photosynthesis, diffusion, and osmosis. the only states that marina had yet to visit were: colorado, wyoming, north dakota, and rhode island. when studying mythology, i learned about several gods and goddesses: zeus, apollo, aphrodite, hermes, and hercules.

The correct answer is - When studying mythology, I learned about several gods and goddesses: Zeus, Apollo, Aphrodite, Hermes, and Hercules.

This is the only sentence which is punctuated correctly because the first part (before the list) ends abruptly; it is obvious that something needs to be placed there. In this case, that is a colon.

The other sentences have leading words (particularly, such as, were) that don't require a colon after them.

it was the battle of midway (june 4-7 1942), in which was an american decisive victory against the japanese navy. americans lost one aircraft carrier, one destroyer and 150 planes. japan lost 4 aircraft carriers, 1 heavy cruiser and 248 planes. american casualties were 307 and japanese casualties were 3057. japan never recovered from its loses and after midway the americans started getting the upper hand in the pacific war.

themselves

an intensive pronoun is a pronoun that ends in self or selves, such as himself, herself, themselves, yourself, ourselves. since band members is a third person plural, the correct intensive pronoun would be themselves. if the band was talked about as a collective noun, itself would be the appropriate intensive pronoun. intensive pronouns are used to add emphasis to the noun it's modifying which is why it directly follows it.