Learn Russian: Обычно она водит нас в старый собор. - Usually she takes us to the old cathedral.

водит is the multidirectional verb for leading or taking someone on foot. We use it here because the word обычно (usually) tells us this is a repeated, habitual action. If she were taking us there right now as a one-time, one-way trip, we would use the unidirectional verb ведёт.

I learned that the verb for 'to take' is брать. Why is this sentence using a form of водить?

In English, we use 'take' for almost everything. In Russian, брать means to physically grab or pick up an object. When you 'take' a person somewhere (meaning you lead or accompany them), you must use transitive verbs of motion like водить (on foot) or возить (by vehicle).

Why doesn't the ending of старый собор change after the preposition в?

The preposition в here indicates direction or destination ('to the cathedral'), so it requires the Accusative case. Since собор is a masculine inanimate noun, its Accusative form looks exactly like its Nominative (dictionary) form. The adjective старый matches this and also stays the same.

What case is нас in this sentence?

It is in the Accusative case. нас is the direct object of the verb водит (she takes whom? - us). It is the Accusative form of the pronoun мы (we).