Learn German: Wo kaufst du den bunten Gürtel? - Where are you buying the colorful belt?

In this sentence, the belt is the direct object (the thing being bought), so it is in the accusative case. Gürtel is a masculine noun. When a masculine noun in the accusative case comes after a definite article like den (the), the adjective describing it gets an -en ending. That is why it becomes den bunten Gürtel.

How can I tell if Gürtel is singular or plural in this sentence, since the noun looks the same for both?

You can tell by looking at the article! The singular masculine article in the accusative case is den, which is what we see here. If it were plural (meaning "the colorful belts"), the accusative article would be die, making the phrase die bunten Gürtel.

Why does the translation say "are you buying" instead of "do you buy"?

German does not have a separate present continuous tense (the "-ing" form) like English does. The single German present tense verb kaufst covers both "you buy" and "you are buying". You just pick the one that sounds most natural in English based on the context.

Why is the verb kaufst in the second position? Do not questions usually start with the verb?

Yes/no questions start with the verb (like Kaufst du den Gürtel?). However, this is a "W-question" because it starts with the question word Wo (Where). In W-questions, the question word takes the first spot, and the verb always stays firmly in the second position.