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Yes, it's legal for US companies to have employees in India (or any other country for that matter).
Have you looked into PayPal as a means to pay them?
Yes, you may very well be inquired about the matter - why your sending them monies. Yes, they would be interested in any money laundering scheme or other illegal activity.
However, if you can pay them as employees regardless of where they reside as employees of your US company. However, you may have to follow their country's rules and regulations by setting up a satellite office and registering to do business there potentially.
You would have to follow their rules and regulations - not just US's.
Are you asking how to send them monies without reporting it?
Although that's not what your question was - you asked, "How can we pay them their salaries from USA and secondly is it legal to have employees in India while having business in USA."
I'm going to opt out and maybe some else can help you.