Income tax question from indian citizen paid from the us

Hello,

I am an Indian citizen who moved back to India from the US to work for a US firm's India office. My offer letter talks of a dollar rate (per hour) plus a nominal payment for training the team in India in rupees. My salary is transferred from the US, along with office expenses, and is, in turn, transferred to me through a bank transfer within India. I have been paying my taxes in accordance with the IT slab provided by the government of India.

My company does not put me in the payroll and does not pay for benefits such as PF and superannuation. Given this, have I overpaid my taxes? Am I entitled to a refund? If so, how do I go about this?

Also, recently, my accounts manager has started to deduct 10.3% from my total salary (dollar component realized in rupees plus the rupee component) every month. Do I have to pay additional advance tax as per the IT slab or is the TDS enough? Am I entitled to any refund of the TDS amount?

Last question - is my dollar component taxable or is the rupee component alone taxable?

Thanks a lot in advance.