Do I need to file a tax return with the IRS or could I go ahead and
close the company by informing the company formations agent ?
Whether or not you need to file the return with IRS depends on what you wrote in the EIN application, but it is likely that if everything was done properly, IRS don't need anything from you other than withdrawal of the EIN.
However, you might be required to file State tax returns in the State in which you organized the LLC, check the State laws.
Also, closing the company is not done by "informing the formations agent", but by informing the State's Department of State or Corporations Commission, or a similarly named government agency. Your formations agent may be able to do that,for a fee, but its nothing you cannot do yourself - and you better do it yourself to make sure its done properly. In some States (California, ahem....) leaving a stale company may rack up thousands of dollars in tax bills very very quickly.
Could I just continue with the company by filling zero tax returns for
another year and would I have to declare my Indian income to the US
If you file a non-resident tax return you may be needed to declare (but not pay taxes on) your Indian income.
If I have to file a zero tax return for this year can I do it after a
terminate the company or do I need to file the returns before shutting
down the company.
Individual tax returns are filed at the end of the year. For LLC tax returns (if the State requires those, or if you declared yourself as a partnership/corporation to the IRS on the EIN request form) - check the relevant requirements.