The subject of the sentence governs the person used in the conjugation.
The subject is 'actividades'. The determiner 'nuestras' only modifies the subject, so it doesn't bear any consideration in verb conjugation.
Since 'actividades' is plural, and it's a referenced object, a third-person, plural conjugation is required. Given this information, I think you know the answer to the question.
As to your other question, the 'verbs' you're talking about are actually gerunds in the English language (words that look like verbs, because they end in '-ing', but act as a noun).
Our favorite activities are watching movies, ....
The word 'watching' is a noun. The Spanish equivalent is the infinitive. You used 'mirar' in your sentence, but you should use ver películas. This is the Spanish equivalent of 'watching movies' (a noun clause).
Welcome to the forums! By the way, I moved your thread to this forum because it sounds kind of like homework.
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