Learn Italian: Ho conosciuto Marco a una festa.

In Italian, the verb conoscere means 'to know (a person or place)'. However, when you use it in the past tense (passato prossimo), it specifically refers to the moment that knowledge started: meeting someone for the first time. If you wanted to say 'I knew Marco' as an ongoing state in the past, you would use the imperfect tense: conoscevo Marco.

Could I say ho incontrato Marco instead?

You could, but it changes the meaning! Incontrare is used for meeting up with someone you already know, or bumping into them by chance. Because this sentence uses ho conosciuto, it specifically means this was your very first time being introduced to Marco.

Why do we use the preposition a for 'at a party' instead of in?

In Italian, social events and gatherings like a party (festa), dinner (cena), or a meeting (riunione) usually take the preposition a to mean 'at'. So 'at a party' is translated as a una festa.

Why does conosciuto end in -o? Doesn't it need to agree with Marco?