Learn Russian: Вы можете смотреть контент и читать каталог офлайн. - You can watch content and read the catalog offline.

You would place the correlative conjunctions directly before the actions you are linking: Вы можете как смотреть контент, так и читать каталог офлайн. This correctly balances the sentence and puts equal emphasis on both available features.

Why does the sentence use the imperfective verbs смотреть and читать instead of their perfective forms?

The sentence describes a general capability or an ongoing feature of a service. You have the general ability to do these actions whenever you want. Perfective verbs (посмотреть, прочитать) would wrongly imply the ability to successfully finish watching or reading a specific, single item.

How does the word офлайн decline in this sentence?

It doesn't decline at all. Офлайн is a borrowed English word that acts as an invariable adverb here. It never changes its ending for case, gender, or number, regardless of how it is used in the sentence.

Why do the direct objects контент and каталог look like they are in the nominative case?

They are actually in the accusative case because they receive the action of the verbs. However, because both are inanimate masculine nouns, their accusative forms are identical to their nominative forms. If the object were a feminine noun like статья (article), it would change to статью.