Learn Russian: Он якобы не читал статью, хотя распространял ссылку. - He allegedly did not read the article, although he spread the link.

The particle якобы means 'allegedly' or 'supposedly'. By using it, the speaker implies that this is what the man claims, but the speaker strongly doubts it is true.

Could we use мол instead of якобы here?

Yes, but it shifts the focus. Мол is primarily used to relay someone else's words like a casual quote (meaning 'He says he didn't read it'), whereas якобы specifically highlights the speaker's skepticism about that claim.

Why are both verbs (читал and распространял) in the imperfective aspect?

For не читал, using the imperfective with negation emphasizes that the action didn't happen at all (he didn't even engage in the process of reading). For распространял, the imperfective shows that spreading the link was a repeated or continuous action, rather than a single completed event.

Since читал is negated, why is статью in the accusative case instead of the genitive case (статьи)?

While negated verbs can trigger the genitive case (the 'genitive of negation'), the accusative case is usually preferred when referring to a specific, definite object. Since they are talking about one specific article, the accusative статью sounds much more natural here.