Two questions: 1) Is jsem pronounced "sem", as if the j is silent? 2) Does pronounciation in Czech always follow hard and fast rules? (Like Polish for example)
It is usually pronounced like that, unless you want to sound really hypercorrect.
I am not sure what you mean by hard and fast rules. I do suggest you to check the tips and notes sections (available on web only atm), especially those for the very first skill.
You have mixed up English and Czech in your sentence.
English "no" is Czech "ne" and English "I am" is Czech "(já) jsem". - No, I am... = Ne, já jsem...
Ne, jsem Žofie is an acceptable answer in the system. It is a good written reply, when spoken most people would squeeze in the pronoun here. If you do not do it, it sounds too much like "Nejsem Žofie" which is quite the opposite of the desired expression.