If you are tax-resident in the US, then you must report income from sources within and without the United States. Your foreign income generally must be reported to the IRS. You will generally be eligible for a credit for foreign income taxes paid, via Form 1116.
The question of the stock transfer is more complicated, but revolves around the beneficial owner. If the stocks are yours but held by your brother, it is possible that you are the beneficial owner and you will have to report any income.
There is no tax for bringing the money into the US. As a US tax resident, you are already subject to income tax on the gain from the sale in India. However, if the investment is held by a separate entity in India, which is not a US domestic entity or tax resident, then there is a separate analysis. Paying a dividend to you of the sale proceeds (or part of the proceeds) would be taxable. Your sale of the entity containing the investments would be taxable. There are look-through provisions if the entity is insufficiently foreign (de facto US, such as a Subpart-F CFC). There are ways to structure that transaction that are not taxable, such as making it a bona fide loan (which is enforceable and you must pay back on reasonable terms). But if you are holding property directly, not through a foreign separate entity, then the sale triggers US tax; the transfer into the US is not meaningful for your taxes, except for reporting foreign accounts.
Please review Publication 519 for general information on taxation of resident aliens.