Learn Spanish (Spain): ¿Adónde vas tan rápido?

Adónde means "to where" and is used with verbs of motion like ir (to go) to indicate a destination. Dónde just means "where" and indicates a location. While you might hear native speakers occasionally say ¿Dónde vas? in casual speech in Spain, adónde is the grammatically correct choice when asking about a destination.

Why use tan instead of tanto in this sentence?

You use tan (meaning "so") before adjectives and adverbs. Because rápido acts as an adverb here, we use tan. You only use tanto (meaning "so much" or "so many") before a noun or after a verb, such as in tanto tiempo (so much time).

I thought adverbs usually end in "-mente". Why is it rápido instead of rápidamente?

While rápidamente is the standard adverb form, it is very common in everyday Spanish to use certain adjectives as adverbs without changing their form. Rápido is frequently used this way to mean "fast" or "quickly". This is just like in English, where we say "going so fast" rather than "going so fastly".