Learn Arabic (Modern Standard): التجديد تلقائي عندما تشتركين في الباقة السنوية. - Renewal is automatic when you subscribe to the annual package.

This is a classic nominal sentence (a verbless "is" sentence). The subject, "the renewal" (التجديد), is definite. The predicate, "automatic" (تلقائي), must be indefinite to create the meaning "The renewal is automatic." If you added الـ, you would get التجديد التلقائي (the automatic renewal), which is just a noun phrase, not a complete sentence.

Who is this sentence speaking to, based on the verb تشتركين?

It is addressing a single female. The ـين (-īna) suffix on a present-tense verb marks the second-person feminine singular ("you", female). If it were addressing a male, it would just be تشترك (tashtarik).

We usually translate "subscribe" with "to" in English. Why does Arabic use في ("in") here?

The verb اشترك (to subscribe, participate, or share) strongly pairs with the preposition في. In Arabic, you don't subscribe "to" a service; you participate "in" it (في الباقة). Learning verb-preposition pairs as a single unit is highly recommended at this level!

Is متى (matā) interchangeable with عندما ('indamā) here?

No, you cannot use متى here. متى is a question word used to ask "When?" (e.g., "When does it renew?"). Because "when" in this sentence connects two clauses as a conjunction ("at the time that"), you must use عندما.