Learn Turkish: Bizim köklerimiz nereden geliyor acaba? - I wonder where our roots come from?

Acaba can go at the beginning or the end of a sentence. Placing it at the end, as in nereden geliyor acaba?, is very common in spoken Turkish and makes it sound like you are thinking aloud, softening the question into a gentle pondering.

Do we really need Bizim if köklerimiz already has the 'our' ending?

You do not strictly need it. Köklerimiz alone means 'our roots.' Adding the pronoun Bizim at the start adds emphasis, showing that the speaker is specifically thinking about their own origins as opposed to anyone else's.

Is kök used for both plant roots and family origins, just like in English?

Exactly! Kök literally means the root of a tree or plant, but it is widely used in a metaphorical sense for family heritage, cultural origins, or even the root cause of a problem.

Why do we use nereden instead of another question word for 'where'?

Nereden means 'from where.' Because the verb is geliyor (is coming), you need the ablative case ending -den (from) on the question word to indicate the starting point of the journey.