Learn Russian: Дети молчали весь урок. - The children were silent for the whole lesson.

It is a verb! In English, we use the verb 'to be' plus the adjective 'silent.' In Russian, молчать is a standalone verb meaning 'to be silent' or 'to keep quiet.' Here, молчали is just the past tense plural form of that verb.

Why is there no Russian word for 'for' in весь урок (for the whole lesson)?

In Russian, you do not need a preposition to express how long an action lasts. You simply put the time phrase in the accusative case to show duration. Because урок is a masculine inanimate noun, its accusative form looks exactly like the nominative.

Why do we use the imperfective verb молчали instead of a perfective form?

The imperfective aspect is used here because the sentence focuses on an ongoing state that lasted for a specific amount of time (весь урок). Whenever you emphasize the continuous duration of an action, you must use an imperfective verb.