1) Is there an age limit to travel alone eg: should be above 10 years atleast ?
No. Young children will need to be in the company of a responsible adult. Older children can travel alone, although airlines require children in a certain age range to use the "unaccompanied minor" service in that case. The details and the specific range of age varies from one airline to another.
2) What letter should parents provide to airline/us-govt to ensure parents approval for travel?
This will depend on the airline, on the country the child is traveling from and to, and on the transit countries, if any. As far as the US government is concerned, a simple letter of permission should be sufficient. It may help if the letter is notarized. The airline or the other countries may have stricter requirements.
3) Is minor allowed to leave US soil ?
Of course. As long as it can be established that the child is traveling with the permission of the parents, and especially if the child is traveling to join the parents, there will be no problem leaving the US. This assumes that the child has permission to be in the country where the parents reside, of course. If the child is not a citizen of that country, it may be necessary to show a visa or residence permit to the airline before the airline will allow the child to board the plane. The details vary depending on the country in question.