Facts:
There is an Indian Company which was formed in 1980s (probably 1983) from Indian funds and assets. At that time it could not remit its profits & sale proceeds
This Company has income from running a Business Centre, dividend (from stocks listed in the Indian stock exchange & mutual funds - both equity & debt), interest , long & short term capital gains in Stocks & Mutual Funds and rent from investment property
Investment in stocks & Mutual Funds (MFs) are listed in the main & other objects of the Articles of the Indian Corporation and are also a business objective of the Indian Company. All these items The dividends & capital gains on stocks & MFs are nearly as much as the income from Business Centre for last 3 years
This Company has not declared any dividend since inception
There are three share holders of the company - father, mother & son. All three share holders are now US citizens but were born in India and are of Indian origion

Our Queries:
Can the share- holder's be taxed in USA on in the income of the Indian corporation even though the corporation has not declared any dividend?
Is the income of the Indian corporation blocked in FY 09-10 from being sent abroad in dollars? If not, in which FY was this condition relaxed?
Is the dividend in the hands of the share-holders blocked in FY 09-10 from being sent abroad in dollars? If not, in which FY was this condition relaxed?
Is the dividend, interest, rent & long term capital gains income of this Indian corporation "passive" or "active"? All these items are listed in the main & other objects of the Articles of the Indian Corporation
Is it correct that under the "Double Taxation Treaty between USA & India, any entity (particularly an Corporation formed by Indian funds & incorporated in India) can only be taxed in one country (i.e. India), where ever it gets better tax treatment. This is important because the tax on dividend income & long term capital gains on stocks is much more favorable for the assessee in India than in USA.
In case the passive income is taxed in USA, at what rate - 1. On the lower rate for qualified dividend & long term capital gains or higher marginal rate? Also will we get credit for the tax deducted (16.95%) by the listed companies declaring the dividend?
Is the income in HUF of India, taxable in the hands of members of HUF in USA?
What tax planning must be done in India to minimize the taxes in USA on income of Corporations (UMS etc.) in share-holder's hands? Should UMS distribute the dividends?

The situation you describe is very complicated and is in fact a real mess.

1) The foreign corporation is a CFC (controlled foreign corporation) by US tax laws and the shareholders should have been declaring a lot of foreign income and making many information filings yearly with respect to this company.
2) The foreign corporation also could be a PFIC, which makes matters even more complicated since then
3) you definitely cannot use more favorable tax treatment under tax treaties. You can take a tax credit for Indian taxes, but you will have to pay the rest in US taxes.
4) I presume the shareholders also had signatory authority on some accounts, so they should have been filing FBARs
5) A HUF is probably something like a family trust, so its even more complicated.

Basically, I think the individuals involved have some SERIOUS tax non compliance issues in the USA. I think they need to immediatedly consult a tax lawyer and a CPA. They might even consider the current voluntary disclosure scheme. They might need to talk to Indian tax professionals for some aspects of this situation.

This is the sort of thing that's going to require tens of thousands of dollars (at least) and lots of research to resolve. You're not going to get an answer here.