Learn Turkish: Tren nereye gidiyor? - Where is the train going?

Because the train is moving toward a destination. Nerede means 'where at' (location), but nereye includes the directional ending -e (with a buffer -y-), so it literally means 'to where'.

Why is the verb gidiyor spelled with a 'd' when the dictionary word is gitmek?

The verb root is git-. In Turkish, when a root ends in a hard consonant like 't' and you add a suffix starting with a vowel (like the -iyor tense ending), the 't' often softens into a 'd'. This makes it gidiyor instead of 'gitiyor'.

Why is the question word nereye placed in the middle of the sentence?

In Turkish, question words usually sit in the exact same spot where the answer will go. Since the answer would place the destination right before the verb (for example, Tren Ankara'ya gidiyor), the question word nereye simply takes that spot.