The phrase
Vi amas kiu?
Is that correct? or should it have an -n on the end of kiu?
Google translate says it shouldn't have one, I believe the -n goes on direct objects, can you determine that kiu is a direct object? I'd say it's not therefore doesn't need the -n.
No, it is not a correct sentence. Either vi or kiu has to take the n-ending, depending on which one of them is the one who is being loved. Without it there is no way of telling which of the two is being loved and which of the two does the loving.
If you want to say “Whom do you love?”, it should be Kiun amas vi? (or some other word order, but usually kiun comes first). If you want to say “Who loves you?”, then it should be “Kiu amas vin?”. The sentences Vi amas kiun? and Vin amas kiu? mean the same thing as the previous respective sentences, but the word order is unusual.
Do not trust Google Translate for these kinds of things.
It is not correct. Subjects of sentences can be identified as nouns, pronouns or correlatives which don't have a preposition before them, and no -n ending. That sentence structure would incorrectly suggest that both vi and kiu are subjects. The only subject in that phrase is vi, so kiu takes the -n ending.
The same would apply in variations of the question, such as: "Vi amas kiun hundon?" "Vi amas kiun vian kolegon?" and to possible responses, such as: "Mi amas tiun" "Mi amas neniun" "Mi amas la princon"
There are cases when a preposition would indicate that kiu is not a subject, in that case no -n is needed: "Vi parolas pri kiu?" "Vi kuras al kiu?"
Or, if kiu would be a subject (who loves you?) then vi gets the -n: "Vin amas kiu?/Kiu amas vin?"
whothat would explain it.