Any Indian citizen with a current account in the name of their business can start a sole proprietorship. Registration may or may not be required, depending on what business you are planning to establish. However, to open a current account, banks typically require a Shops & Establishments Registration.
To open a current account, you need proof of the existence of your business. Most banks will ask for a Shops & Establishments Act Registration. In addition, you will need a PAN card and address and identity proofs.
A sole proprietorship business does not take more than 15 days to open-up and get running. This simplicity makes it popular among the small traders and merchants. It's also much cheaper, of course. This is the other reason why it's the most widely used business structure.
Most local businesses are run as sole proprietorships, from your grocery store to a fast food vendor, and even small traders and manufacturers. This is not to say that larger businesses do not operate as sole proprietors. Even some jewellery shops are sole proprietors, but this is not recommended.
To start a sole proprietorship, you would need address and identity proofs, PAN card, all KYC documents and rental agreement or sale deed (in case of Shops & Establishment Act Registration).
This depends on the business you're in. If you're running a departmental store, then you would also need a VAT Registration once your turnover is over Rs. 5 lakh per annum. If you're running a air-conditioned restaurant, you would need a VAT Registration and Service Tax Registration.
The registrations controlled by the central government -- service tax, for example -- can be availed of online, whereas the state-government-controlled ones may or may not be. In some technologically advanced states, such as Karnata, they are, whereas in others they may not be.
You can always choose to do so. The procedure is a little tedious, but it is possible. It is very common for sole proprietors to convert into partnerships and private limited companies at a later stage.
A Sole Proprietorship is inexpensive as compared to a One Person Company (OPC) and, thanks to the minimal compliance requirements, is inexpensive even over the long-term. You would not need to hire an auditor, for example. This is why, despite its severe shortcoming (unlimited liability), small merchants and traders opt for it.