Learn Russian: Ты будешь работать, а я буду отдыхать.

This is how you form the compound future tense in Russian! You conjugate the helper verb быть (to be) to match the subject—будешь for ты and буду for я—and leave the main action verb in its infinitive form (работать, отдыхать).

The translation says "and I will rest", but isn't the Russian word for "and" usually и? Why use а here?

You use а when you are drawing a contrast between two things. While и just adds information together, а means something closer to "whereas" or "while on the other hand." Since "you working" and "me resting" are contrasting situations, а is the perfect word to connect them.

Could I use a perfective (completed action) verb instead of the imperfective verbs работать and отдыхать?

No, the helper verb быть (will) can only be used with imperfective verbs. This structure focuses on the ongoing process of doing something. If you want to use a perfective verb to show a completed result in the future, you do not use быть at all—you just conjugate the perfective verb directly.

Since будешь and буду already tell us who is doing the action, could we drop the pronouns ты and я?