How to open a trading business in USA by a Indian Citizen?
Yes, you would be able to register and conduct your business without being a United States' citizen. Also, most states allow any physical address in the world (with a few exceptions) to be listed as the principle business address. If you already have serious plans to establish physical presence in a specific state (like having an office, warehouse, etc), that state would probably be the best candidate to register your company in. If you have no plans to establish physical presence (or still undecided as to which state that would be in) I would strongly recommend forming your business in states such as Delaware or Wyoming.
When it comes to importing/exporting, once you complete your business registration and your business obtains it's EIN, you might need to apply for some licenses: a state sales tax ID (if the state of formation has sales tax), and an exporting license, if the goods you plan to export from the US require such licensing. Once you have your business registered and all the appropriate IDs and licenses obtained, you would be able to carry your business plans exactly as you want to.
This is definitely something we could help with - everything from the initial business registration, the EIN (we can get your business an EIN without a social security number) to all of your specialty licensing and filing needs.
I hope you find this answer to be helpful.