Learn Polish: Zjemy wszystko z wyjątkiem mięsa. - We will eat everything except for the meat.

The phrase z wyjątkiem is a compound preposition that means "except for" or literally "with the exception of". It always requires the noun that follows it to be in the Genitive case.

I thought the preposition z takes the Instrumental case. How does that work in z wyjątkiem mięsa?

It actually does! The word wyjątkiem is the Instrumental form of the noun wyjątek (an exception). So z wyjątkiem literally means "with an exception". However, as a set phrase, it acts as a compound preposition that demands the following word (mięsa) takes the Genitive case. This is very similar to how we say "with the exception OF meat" in English.

What is the difference between saying zjemy and będziemy jeść in this context?

Zjemy is the perfective future tense, meaning the action will be completed. It implies that we will eat up or finish everything on offer. The imperfective będziemy jeść would just mean "we will be eating", focusing on the ongoing process rather than the completion of the meal.

Is wszystko in the Nominative or Accusative case in this sentence?

It is in the Accusative case because it is the direct object of the verb zjemy. For neuter pronouns like wszystko, the Accusative form is identical to the Nominative form.