In Cerro Castillo there is a very small border crossing that is open year round from 08:00 to 22:00. I've crossed this border in January 2014 with a rental car, since at least at this time, there was no direct public bus from El Calafate over Cerro Castillo to the National Park. All public buses go over Puerto Natales. However, maybe, it might be possible to get a seat on a bus from El Calafate to Puerto Natales and get off at Cerro Castillo and then get another seat on a bus from Puerto Natales to Torres del Paine. Then you would save a couple of hours. On the other hand, it seems a little bit risky.
There are private bus companies, like for example this one, that offer regular routes from El Calafate to Torres del Paine, without going to Puerto Natales first.
As a last resort, you could also drive their with a rental car. For more information about this option, check out this question.
So in summary:
1) Yes, there is a border crossing in Cerro Castillo, open to the public from 08:00 to 22:00 each day.
2) Probably, there are no direct bus connections, avoiding Puerto Natale, however, there are privat bus companies that offer direct connection from El Calafate to Torres del Paine.
3) You could also rent a car and drive there.