Agree on grounding the 7-way directly. Remember that the light converter, even though powered, only deals with the lights. I suspect that the light converter only needs power for its internal circuitry, since power to the lights will come into the converter box from the vehicle lights it is connected to.
The brakes are going to be fed by a separate power line coming from the battery (or switched power source) directly to the brake controller. If you are including a 12v+ charge line, that will be a separate feed from the battery, so 3 battery connections in all for this 7 pin connector.
If you are not towing anything that has brakes, then stick with the flat 4 connector.