What's the difference between Ty jsi Zofie and Jsi Zofie?
You can emphasize Ty or not, it is not necessary there.
It is almost same, Ty = You
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.