Incorporating LLC in US
We can definitely help you register an LLC in the United States, along with obtaining all the documentation necessary to open the company bank account. I invite you to read our article dealing with foreigners opening a bank account in the US.
As India is a signatory of the Hague convention, we can get your company an Apostille, which would allow your U.S.registered business to be recognized in India. Maybe you could check with your bank of business and see if that would help your situation any.
By forming an LLC, which is a pass-through entity, the income will pass through the entity directly to the owner's personal income. We offer a free tax-webinar for U.S. business owners living abroad, that may help answer some of the common tax questions.
Regarding the TDS, which I believe you are referring to Tax Deducted at Source, so this is something you should consider consulting with an accountant.