A person who is Non Resident under the Provisions of The Income Tax Act, 1961 has to pay tax on the income earned from any source in India. Income source could be interest, dividend or short-term capital gains (less than one year holding period) from investments in India etc.

Yes, there are exemptions. NRI does not have to file taxes if:
• Tax has been deducted at source (TDS) from the income earned in India.
• Source of income comes from long-term capital gains. Long-term capital gains arise from sale of investment held for more than    one year.

Please remember that tax deducted at source (TDS) gets deducted at the highest possible income tax rate. However, ultimate tax liability can be lower due to the following:

• Capital losses can be set off against capital gains but tax gets deducted from capital gains without setting off the losses.
• Reinvestment of capital gains may exempt NRI from paying taxes on the capital gain but the tax gets deducted at the source    when capital gains are received.
• Standard deductions can lower ultimate tax liability.
• If NRI's country of residence (say USA) has double taxation treaty with India, than NRI pays the lower of tax rate deducted at   source or the tax rate prescribed by double taxation treaty.

It's a good idea to file tax returns (it's called Return On Income (ROI) in India) in India, if any of the bove applies and the ultimate tax liability is less than the tax deducted at source. You may get a refund.

Yes, you have to report your foreign earnings on US tax return. However, you can claim credit for taxes paid in the foreign country (in this case, India) by completing IRS form 1116 while filing taxes in USA. Credit applied on form 1116 will be equal to tax paid in India. Be sure to pay lower tax rate in India by taking advantage of lower tax rates available in Double Taxation Avoidance Agreements (DTAA).

In India, Individual income tax is a progressive tax with three slabs.
From April 1, 2010 new tax slabs apply, which are as follows:
   • No income tax is applicable on all income up to Rs. 1,60,000 per year. (Rs. 1,90,000 for women and Rs. 2,40,000 for senior       citizens)
   • From 1,60,001 to 5,00,000 : 10% of amount greater than Rs. 1,60,000 (Lower limit changes appropriately for women and       senior citizens)
   • From 5,00,001 to 8,00,000 : 20% of amount greater than Rs. 3,00,000 + 14,000 (slightly less for women and further less for       senior citizens)
   • Above 8,00,000 : 30% of amount greater than Rs. 8,00,000 (slightly less for women and further less for senior citizens)

Yes. India has tax treaties with other countries. These are called The Double Tax Avoidance Agreements (DTAA) and their objective is to avoid taxation of income in both the countries. It results in lower tax deducted at source (witholding taxes) and tax credit when tax has already been paid in one country. Here is the link to US India Tax treaty.