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Questions & Answers about Ich gehe nach Hause.
Which question word does this sentence answer: wo, woher, or wohin?
It answers wohin (where to). Because you are expressing movement towards a destination, someone would prompt this by asking Wohin gehst du? (Where are you going to?).
Why does the sentence use nach Hause instead of zu Hause?
Nach Hause is a directional phrase that means "towards home" or "homewards", which pairs perfectly with the verb gehen (to go). Zu Hause is locational and means you are already at home (answering wo).
Why is there an "e" at the end of Hause instead of just using the normal word for house (Haus)?
That extra "e" is a leftover from old German grammar. Hundreds of years ago, nouns often got an extra "e" ending after certain prepositions. The rule died out, but it survived in a few very common, fixed expressions like nach Hause (going home) and zu Hause (at home).
The English translation says "I am going", but the German just says Ich gehe. Where is the "am"?
German doesn't have a separate "-ing" form (present continuous tense) like English does. The simple verb form gehe translates to both "go" and "am going" depending on the context.