As a resident alien, you have to report worldwide income in your tax return.
1 You need the details of income like interest, the dividend for the calendar year.
2. You gather all relevant information and enter the foreign taxes paid in form 1116 to claim credit for the taxes paid in India. You will have to file FBAR with FINCEN if your deposits in India are more than $10000.
3. You have to report all the income here in the USA irrespective of whether it is taxable in India.
4 Yes you will be able to apply for the foreign tax credit
5 You have to follow the rules of your home country but report worldwide income here.
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Where do I enter Foreign Tax Credit Form 1116
FBAR
