Learn German: Ich mag den Hype um diesen Sänger nicht. - I do not like the hype around this singer.

Just like many verbs, some nouns are paired with specific prepositions. Here, the noun der Hype pairs with um to mean 'the hype about' or 'the hype around'. The preposition um always forces the following noun phrase into the accusative case, which is why we see the masculine accusative form diesen Sänger.

Does the prepositional phrase um diesen Sänger belong to the verb mag or the noun Hype?

It belongs directly to the noun Hype. The phrase den Hype um diesen Sänger acts as a single, large noun phrase that serves as the direct object of the sentence. If you wanted to change the word order to emphasize the object, the entire block would have to stay together: Den Hype um diesen Sänger mag ich nicht.

Hype is an English loanword. How do German speakers determine its gender, as seen with den Hype?

English loanwords often take the gender of their closest German equivalent (like der Wirbel), or they default to masculine. In this case, it is der Hype (masculine). Since it is the direct object of the verb mag, it takes the accusative masculine article den.

Could I put nicht right after mag instead of at the end of the sentence?