First off, you need to make sure that Russian Consulate general in NY will agree to even consider your friend's visa application. In many instances they only consider applications for visas from actual RESIDENTS of NY state and the states surrounding NY. Same story with other Russian consulates in the States. You may want to call the consulate in question first. Most likely she can only get Russian visa in India.

You cannot make a faux hotel booking and not stay at the hotel when traveling to Russia without consequences. Upon arrival to Russia, your friend's visa will be registered by the hotel at the local OVIR service, and when he/she checks out from the hotel, her/his visa will be stamped by the hotel. Your friend will have serious problems at Russian immigration upon leaving the country if he/she did not stay at the hotel that sent the invitation.

Remember, your friend can stay in Russia without registration only for up to 72 hours.

Visa services work excellent in the US, but as I mentioned earlier your friend's visa will most likely have to be processed in India, I don't know anything about Indian visa agencies.

You are correct, you have to be isnide the country to get an "invitation" for a foreigner, however your family members can get one as well. In this instance, your friend will have to go to OVIR and register her/himself upon arrival within 72 hours from landing, and as you know, Russian OVIR's are a major pain.

With that said, PM me if you have any further questions, and good luck.