Learn Russian: Мой старый друг едет на стадион.

In Russian, open-air public places and events usually take the preposition на (onto/at) instead of в (into/in). Since стадион (stadium) is a large open space, we say на стадион.

I thought the Accusative case changes noun endings. Why is стадион spelled the same as its dictionary form?

While feminine nouns change their endings in the Accusative case, masculine inanimate nouns (objects and places, like стадион) do not change. They look exactly like their Nominative (subject) form.

If I want to ask 'Where is he driving?', which question word should I use?

You would use the destination question word Куда (Where to). The question would be: Куда он едет? Remember not to use Где (Where at), because Где is only for asking where something is currently located, not where it is moving towards.

Why does the sentence use едет instead of идёт?

едет comes from the verb ехать, which specifically means to go by transport (like driving a car, taking a bus, or riding a train). идёт means to go by foot. The sentence tells us the friend is using some kind of vehicle to get to the stadium.