Timur, Emin'in babası. - The subject is Timur, at this point. You're presenting him to the asker. Emin'in babası Timur. - Just a casual way of saying "Emin's father is Timur." There are NO difference. You can use both of them. But "Kim Emin'in babası?" doesn't sound natural. It's not 100% wrong but like I said, it sounds weird. Although inversion forms are used in Turkish, the question sentences shouldn't be upside down. Otherwise, they don't sound right.

in fact we must use( , ) between Timur and Emir. Timur , Emir'in babası.

Very clear, thanks a lot.

In Turkish, the order of the words is not strict. Just like Russian. Though there is a nuance. The last word is stressed more. In other words, by changing the order, you change the important (stressed) word of your statement.

you shoud ask with this way : ' Emir'in babası kim?'