Do you remember the phrase:

Обо мне ещё писали в «Искусстве кино».

As you might have noticed, we don’t use the word «журнал»/magazine (в журнале «Искусство кино»). In a conversation we often omit explanatory words such as газета/newspaper, фильм/film, спектакль/show, балет/ballet, опера/opera if everyone understands what we are talking about. In this case the title of a magazine, newspaper, ballet, etc. is used in the Prepositional case.

Vera says proudly about herself:

Я ведь лучшая актриса киноэтого года.

We Russians are actually very emotional people so in our informal speech we use a lot of special little words like ведь that don’t have any specific meaning but are used to express emotions of the speaker, putting an emphasis on some information. In our case, Vera is saying that mum and dad probably don’t know yet about her being the best actress of the year, so she wants to put an emphasis on this information because it is important for her.

The mum notices:

Такое кино любят молодые.

The words молодые/the young, русские/the Russians in Russian can be used as nouns (substantivized adjectives) and answer the question кто?/who?

Take a look at the title of the film that Vera is talking about: «О любви». The word любовь/love loses the "о" when it’s in the Prepositional case — о любви.