As you are a US citizen, you will be treated as a resident for tax filing in US. In case an individual is a resident of both the countries then tie breaker rule will be applicable as per Article 4 of DTAA.
Assuming you become resident in India as per tie breaker rule and your residential status is ROR then
1) US salary would be taxable in India. FTC (Foreign tax credit) is available proportionate to tax payable in india on salary income
2) LTCG is taxable at special rate. LTCG on sale of equity shares or equity oriented mutual funds is taxable at 10% after exemption of Rs. 1lac. No benefit of indexation is available. Other LTCG is taxable at 20%
3) Dividend and Interest income would be taxable at normal slab rates
4) You are also required to disclose foreign assets and foreign income in Schedule FA
5) If your income is more than Rs. 50 lacs, Schedule AL is also applicable
6) To claim FTC, you will be required to fill Schedule FSI and TR. Also file Form 67 before filing of ITR
For detailed discussion you may opt for phone consultation