Do we need to register to any party in order to run e-business?

No need to register, anyone can sell their products via Internet as long as its not illegal.. but if you are going serious with the business and to make customer more confident, better register as a company.. at least as Enterprise.

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www.shopbegins.com
sell products with your dotcom

For running any e-business you need to have a site with good products which you can sell through, for making financial transaction you also need some reliable payment gateway such as Paypal so that your clients can make payments.
To build confidence for making financial transactions try to get SSL certificate for your site so that all the transactions would be secure.
Most important get a reliable host who can host your site and keep it live round the clock without any downtime.

any product you would like to sell?

what kind of E-commerce engine you wanna to use?

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I blog my IT Engineer LIFE at iCalvyn.com

u better register a trading type company before start