Learn Russian: Мы хотим узнать все подробности самого скандального развода. - We want to find out all the details of the most scandalous divorce.

You could say Неужели мы хотим узнать все подробности самого скандального развода? (Do we really want to find out all the details...?). The particle неужели usually goes at the beginning of the sentence to show genuine surprise or doubt about whether this is actually what we want.

Why are the words самого скандального развода in the Genitive case here?

They are answering the question 'details of what?'. After the noun подробности (details), you need the Genitive case to show possession or relationship, which acts just like the English preposition 'of'.

I know самого comes from the word самый, but what is its function right before the adjective скандального?

Placing самый (in the correct case, here the Genitive самого) directly before an adjective creates the superlative degree. It changes 'scandalous' into 'the most scandalous'. Notice that both самого and скандального must match the noun развода in gender, number, and case.

Why use the perfective verb узнать instead of the imperfective узнавать?