What's the difference between Ty jsi Zofie and Jsi Zofie?
You can emphasize Ty or not, it is not necessary there.
How come the first translation to TY JSI is "are you"? but the answer is "You are"
"Ty jsi" can be both a question or a declaration depending on the intonation (and in written text depending on . or ?).
Ty jsi Žofie? Are you Žofie?
Ty jsi Žofie. You are Žofie.
The word order in Czech is quite free.
So why was 'are you Zofie' marked incorrect?
That is a question word order.
Why use "ty" (or já, on, etc) if it's not necessary? Do Czech use it a lot when speaking or is it just to emphasize?
It is used quite often. To emphasize.