I would not be at all surprised to learn that concierges get kickbacks for restaurant recommendations, but remember that the restaurant would have to have some way to know that you've arrived via the efforts of the concierge. So if the concierge says, "here's a card to give them when you arrive, to assure you can get a table," it's more likely there's a kickback involved. This can also be the case if the concierge calls the restaurant to make the reservation for you. Of course, that may be something you want him to do, so you may not be able to detect it in such a case.

On the other hand, I've gotten restaurant recommendations from concierges before where I'm certain there was nothing involved beyond just the concierge's best recommendation for a good place given the criteria I listed. So I'm sure it's not a hard and fast rule - in fact in my experience I'd guess there have been only about 10-20% of the times when I thought something like that was going on. I think there are other services that may at times involve kickbacks, as well, though - not just restaurant recommendations.

Regarding the second question, if you call the Platinum concierge for services like those a hotel concierge would perform (theater tickets, restaurant reservations, etc.), in my experience the person you talk to on the phone will contact the hotel concierge at the Starwood hotel closest to the service you're requesting and have them perform the service for you. You'll likely be put in direct contact with the on-site hotel concierge.