Learn Russian: Если ты не понимаешь суть проблемы, то не спорь. - If you do not understand the essence of the problem, then do not argue.

It actually is in the accusative case! Суть (essence) is a feminine noun ending in a soft sign (3rd declension), so its nominative and accusative forms are identical. Because the verb is negated (не понимаешь), you could technically also use the genitive case of negation (сути), but the accusative is very commonly kept in modern Russian when referring to a specific, well-defined concept.

Why is the imperative не спорь in the imperfective aspect?

As a general rule in Russian, negative commands (telling someone not to do something) almost always use the imperfective aspect, even for a specific, one-time situation. Using a perfective verb with a negative imperative usually expresses a warning about an accidental action (meaning 'careful, do not accidentally argue'), which does not fit the intention here.

Is the word то mandatory in the Если ..., то ... (If ..., then ...) structure?

It is not strictly mandatory, and you could easily drop it: Если ты не понимаешь суть проблемы, не спорь. However, using то is extremely common and natural in Russian to firmly connect the condition to the consequence, much like adding the word 'then' in English.

Since this lesson is about predicative pronouns like таков, how would we say 'Such is the essence of the problem'?