TDS applicability

If the company pays salary directly to the employees DTAA with USA will have to be seen. If as per DTAA salary is required to be taxed in USA then the company will pay salary after deducting the adequate TDS as per the income tax norms of USA or DTAA whichever is applicable. Otherwise the company will pay the entire amount as salary and the recepient shall file his income tax return in India and pay the required tax (The recepient being an Indian resident).

However, as evident in this case, if the USA company pays salary to its employees in Indian rupees (through an agent appointed in India) then the agent will be required to deduct TDS as per the Indian Income Tax Act.

The company will have to file its income tax return if it has a permanent establishment in India or it carries out any of its working in India. But since no billing is being done from India, there does not arise any such requirement. 

There will not arise any service tax liability. In case of non resident service providers, the liability to pay service tax lies on the service receivers in India. In this case the service receivers are also non-residents, therefore no service tax liability.