Foreign salary income - tds query

Hi 

We have an employee who just joined from US. He is a ROR for this FY. He has an income of 40,000 USD until the date when he joined us and has 8000 USD tax deducted on it. 

I have the following queries:

1. As his Indian employer, should I deduct TDS on his total income (Foreign + Indian) or only Indian?

2. If I consider global income, should I give him the benefit of foreign tax as per DTAA or should I deduct total tax and make him claim relief in his ITR? This can lead to heavy tax burden on him.

3. Can he claim US state tax under section 91? 

Thanks for your response. I can't find answer to Q2 anywhere.