Learn Russian: Благодаря скандалу в сети обсуждают их развод. - Thanks to the scandal, they are discussing their divorce online.

This is an indefinite-personal clause, which is exactly what this lesson covers. By leaving out они (they), the sentence shifts the focus to the action itself or to people in general. It often translates best as 'people are discussing' or as a passive construction like 'their divorce is being discussed.'

Isn't благодаря usually used for positive things? Why is it used with a scandal here?

You are right that благодаря (which requires the Dative case, hence скандалу) literally means 'thanks to' and usually implies a positive outcome. However, in modern Russian, it is frequently used neutrally to mean 'as a result of' or 'driven by,' even with negative words. To sound strictly negative, you would use из-за скандала (because of the scandal) with the Genitive case.

Is в сети the standard way to say 'online'?

Yes, в сети (literally 'in the net') is a very common way to say 'online' or 'on the internet.' You will also hear в интернете, but в сети is especially natural when talking about social media or viral topics. Note that сеть is a 3rd-declension feminine noun ending in a soft sign, so its Prepositional case ending is -и.

If I wanted to say that specific people are discussing the divorce, how would this change?