Ta shi Shei ?
A) Ta shi shei ?
B) Ta shi wo Baba.

I understand this perfectly,
Who is that ?
Thats my Father.

However how would I say Who is your Chinese Teacher ?

Shei shi nide Zhongwen laoshi ?

Or

Ni de Zhongwen laoshi shi shei ?

Or are both okay ?

XieXie

Tommo

Question

Ta shi Shei ?
A) Ta shi shei ?
B) Ta shi wo Baba.

I understand this perfectly, 
Who is that ?   
Thats my Father.

However how would I say Who is your Chinese Teacher ?

Shei shi nide Zhongwen laoshi ?

Or

Ni de Zhongwen laoshi shi shei ?

Or are both okay ?

XieXie

Tommo

Answer

ni hao .,Tommo :

Shei shi nide Zhongwen laoshi ? Or  Ni de Zhongwen laoshi shi shei ?

Dou ke yi ( both are ok).

sophie

Answer

I found that we usually put question words at the end when you use pronouns.
Like
Zhe Shi Shen Me?
Ta Shi Shui?
If you use a noun, both sequences will be O.K.

Answer

Both are ok. But the much politely way to say is "ni de lao shi shi na wei?" or "na wei shi ni de lao shi" 
"na wei" means the same as "shui".

Answer

"shui" ist the most correct pronunciation, but "shei" can also often be heard in North of China~

Answer

As Sophie said, both are right.

Also, I need to tell you that. It's not "shei", but "shui (谁)"