Learn Russian: Мы созваниваемся каждый день.

In this lesson, you are learning about reciprocal verbs. The -ся ending here doesn't mean doing an action to yourself (like washing or dressing), but rather doing it to each other. It changes the meaning from "to call" to "to call each other".

The lesson is about using these verbs with с plus the Instrumental case. Why isn't there a с in this sentence?

You only need с (with) plus the Instrumental case when you are naming the specific person you are interacting with, for example: Я созваниваюсь с братом (I call my brother / My brother and I call each other). Because the subject here is just Мы (We), the "each other" aspect is already fully covered by the plural subject, so no extra preposition is needed.

I know the verb звонить (to call). How exactly does созваниваться change the meaning?

Звонить is a one-way action: person A calls person B. Созваниваться adds the prefix со- (which means "together", like "co-" in English) and the reciprocal ending -ся ("each other"). It specifically describes a two-way connection or a mutual habit of talking on the phone.

What case is каждый день in, and why?

It is in the Accusative case. In Russian, when you talk about how often something happens (like "every day", "all week", or "every year"), you use the Accusative case without any prepositions. Because день is a masculine, non-living noun, its Accusative form looks exactly the same as its dictionary (Nominative) form.