We can assume that the rather odd logo is a symbol of Starfleet's mental health services.
Hmmm. I never picked on up any indications that the penal colony was part of Starfleet.
Doves are usually symbols of peace and hope. The hand reaches up for it towards the sun, a symbol of life. So, strive to hope and heal.
I always took it that the hand was holding the bird, presumably releasing it to fly toward the sun. But it could also be interpreted as catching the bird and stopping it from flying to the sun. Kind of ambiguous.