είναι is "is", not "has" -- that would be έχει.
At best, it could be "She is your sock", but "This is your sock" is a rather more likely meaning of that sentence.
"This" can be αυτός, αυτή, αυτό depending on the gender of "this" -- neuter αυτό if unknown, as when introducing something new, but here presumably it's already known that we're talking about a sock (a feminine noun) and the new information is that this particular sock is your sock. "This one" might also be a translation for αυτή here.
No, it is exactly the same order as in English, with the exception of the Greek possessive that goes after the noun and the presence of the article of course.
this is the sock [that is] yours?
That would be Αυτή είναι η κάλτσα που είναι δική σου. And you cannot omit 'that is/που είναι' in either language in this structure.