Dual citizenship needn't impact retirement dues

Can a US citizen, after obtaining dual citizenship, receive the same retirement benefits from the state if she or he chooses to live in India? Also if one is interested in buying property in India, can one send money directly to the seller in instalments?
Dual citizenship is unrelated with the retirement benefits receivable from India and also is unconnected with where she or he lives. As regards social security benefits, since you continue to be a US citizen, you should still get the benefits. And yes, remittances from abroad towards the purchase of property in instalments are possible depending upon its acceptability to the seller.

Over the past few years, I have been investing in Indian mutual funds. Now, I have received a letter from the income-tax office requiring me to explain the source of the funds invested along with documentary evidence, if any. As an NRI, do I have to show source of my income to the department?
The Indian Income Tax Department has started issuing such letters to many investors on the basis of Annual Information Returns (AIR) required to be provided by organisations like mutual funds in respect of some stipulated transactions. Do not worry much about this. All that you have to do is to submit the photocopies of your bank statements to prove that the funds used for investment originated from your income abroad, which is not taxable in India since you are an NRI. This exercise is more to do with anti money-laundering measures taken up by the tax department and it is just to ensure that the funds brought into the country are from legitimate sources and not tainted. If your India income (less exemptions and permissible deductions) is less than `1.80 lakh, in a financial year, you do not have to file tax returns. If the value of your investment has gone up it does not mean you have earned any profit unless you have encashed the same.