Learn German: Wir nicken, da wir einverstanden sind.

While da is often a location word meaning "there", it is also a subordinating conjunction meaning "since" or "because". Just like weil, it kicks the conjugated verb (sind) to the end of its clause. You will often see da used instead of weil when the reason is already known from context or when translating to "since" in English.

Can I use the verb zustimmen instead of einverstanden sein to say "we agree"?

Yes, you could say ..., da wir zustimmen. However, einverstanden sein (literally "to be one-understanding" or "to be in agreement") is very common when expressing a general state of mutual consent or being okay with a plan. Zustimmen is more often used when actively agreeing with a specific person or statement, like Wir stimmen dir zu (We agree with you).

How would I express the opposite—that we disagree or disapprove—using a miss- prefix verb from this lesson?

To say you disapprove, you could use missbilligen. If you misunderstand, you'd use missverstehen. For example: ..., da wir es missbilligen (..., since we disapprove of it). Because miss- prefixes are inseparable, these verbs don't split apart; they are simply pushed to the end of the clause as a single word by the conjunction da.

Why is sind at the very end of the sentence?