Learn Dutch: Het appartement op de tweede verdieping is erg ruim. - The apartment on the second floor is very spacious.

Usually not! In Dutch, the street level is the begane grond (ground floor). The floor above that is the eerste verdieping (first floor). Therefore, the tweede verdieping is two flights of stairs up—which Americans would call the third floor.

Could I use groot instead of ruim here?

You could, but they have slightly different meanings. Groot simply means "big" or "large." Ruim specifically means "spacious" or "roomy," emphasizing that there is a lot of free, open space inside the apartment.

How would I apply this lesson's grammar to say "The apartment on the second floor in which I live is very spacious"?

You would say: Het appartement op de tweede verdieping waarin ik woon is erg ruim. Because an apartment is an inanimate object, Dutch combines waar + in to make waarin (in which), and sends the verb woon to the end of the relative clause.

What happens to the word order if I move op de tweede verdieping to the very beginning of the sentence?

If you start with that location phrase, the verb must stay in the second position (this is called inversion). The sentence would become: Op de tweede verdieping is het appartement erg ruim.