Yes if you are dealing in India then it's important to have a work place

You can incorporate private limited company as subsidiary of foreign company 

2)The preferred legal entity structure for foreign companies is to establish a company with three Directors, two being foreign nationals from the parent company and one director being a local Indian citizen. Since there are no requirements for minimum shareholding with the Indian Director, foreign nationals or entities can hold 100% of the shares of the Indian Company.

3) Registration of Branch Office, Liaison Office or Project Office requires RBI and/or Government approval

Any Indian or foreign national can set up either C-Corporation (Company) or LLC (similar to that of LLP) in USA. There’s another entity type called an ‘S-Corporation’ but that entity requires all shareholders to be US Citizens. There is no restriction on the number of owners for a US Corporation or LLC, which country the owners are from or whether they are individuals or other companies.

Corporations are responsible for paying tax on their profits and on dividends the entity distributes to its shareholders. Since dividends are not tax deductible, dividends are taxed twice.

Your company or the individual owners may have to pay taxes on any US-based income. There are 2 type of taxes one is state level and another is federal level. In addition many states are charging franchise tax. You should be in touch with your registered agent for tax compliance.

There are no restrictions on foreign ownership in a US-based LLC or a Corporation. The procedure for a foreign citizen to form a company or become a partner in a US-based firm is the same as for a US resident. It is not necessary to be a US citizen or to have a green card to own a corporation or LLC.  You register a company in the US where you have access. A non-US resident foreign citizens or foreign companies can open a company in the US -as a single-person owner. You do not need to have a partner in order to open up a company in the US. You can work from India in any capacity in your company in the US. Once your business grows you can apply for L-1 Visa after fulfilling certain requirements. In case you get an L-1 visa, you can stay in the US and also apply for your Green-card through your own company. Every state may offer different benefits or may have different tax formalities. The Federal Income Tax rate can vary depending on the income of corporations. rate depends on the net profit and not on the revenue. 

The capital gains tax regime in India works in such a way that all Indian tax residents are taxable on their worldwide income, including income in the nature of capital gains arising from disposal of a foreign asset. However, all non-residents are taxed in India only on India-sourced income i.e. capital gains arising from the disposal of an Indian asset. Similarly, in the US, all US citizens and resident aliens for tax purposes are taxed on their worldwide income in form of capital gains However, non-residents are not taxed in the US for disposal of all US-sourced assets.

Start a business is India as per Indian law

Government of India has put in place a policy framework on Foreign Direct Investment. NRIs, PIOs, Overseas Citizens, or Foreign residents or nationals are allowed to invest in India either by buying shares in an existing Indian company or registering an entirely new company. Now coming to FDI, there are two routes:

• 
  Automatic Route: Does not require the permission from the RBI or Indian government. The 100 percent automatic route includes sectors like the Infrastructure Company in the Securities Market, Insurance, Medical Devices, Pension, Petroleum, etc.
• 
  Government Route: Prior approval from the government is mandatory. To increase the speed and transparency in the FDI approvals, Foreign Investment Promotion Board (FIPB) has been replaced by the Foreign Investment Facilitation Portal (FIFP) which functions as the online single-window clearance for the incoming  FDI proposals in consultation with the respective ministry and the Department of Policy and Promotion (DIPP). Only 11 sectors such as defense, retail trading, etc require government approval.

You can open branch office in India. 

Dear Client, 

It is not mandatory to have a branch in India if you starting in US. The legal procedures required are - Once you have created a memorable business name, you must register that name in your community. Licenses for travel agents are dependent upon state regulations. Some states, like California, require agents who "sell, provide, furnish, contract for, or arrange the retail or wholesale sea or air transportation" to attain a “Seller of Travel License.” And the next is certification. 

Thank You