1. For execution, if both parties happen to be in either of the place, viz. in India or U.S. then the agreement can be simultaneously executed, at the place, mentioning the place. If it is in India, you may use the stamp paper of appropriate value OR get the document franked. If franking - get this done before execution by the parties.
2. If the agreement has to be signed by parties @ different places - firstly get the agreement executed on plain paper @ U.S., with two witnesses and once it is received in India, present the document before the stamp authorities, for franking with appropriate stamp value. After this franking is done, the service provider @ India can execute this. In such case, the execution dates would be different, but the date of coming into for of the agreement can be set out in the agreement.
3. As for the jurisdiction, the parties may chose the jurisdiction mutually agreed between the parties.