"She is a sister."
Translation:Ea est soror.
No, there is no object when the verb is stative. Only active verbs can take objects. "Sister" is the subject complement. Notice how it's in the nominative and not the accusative.
In Latin, the typical syntax is Subject Object Verb. But when the verb is stative, such as "esse", the subject and the subject complement are both in the nominative. Therefore to better differentiate between the subject and the subject complement, the syntax becomes Subject Verb Complement.
That's not true. The verb "est" is not like the other verb. Most of the time it is supposed to be in the middle of the sentence (or at the beginning), this verb is rarer at the end of the sentence, unlike the other verbs.
The meaning is slightly different when you change the word order, it changes the emphasis.
"Ea est soror" is the most common word order in Latin. And "Est soror" is the most common way to say it.