Let us know your location - it will help with general advice!
Your dawn redwood looks a little beaten up, but that might be a function of the stress of shipping as much as anything, particularly if the tree was being grown in a protected environment like a greenhouse. The damage I am seeing appears to be physical.
A couple of comments:
(1) make sure you don't rot the roots. It appears that you are keeping the tree in a tray of standing water. Unless you are keeping a semi-aquatic tree like a bald cypress, you need to make sure that your soil does not become saturated. Roots need oxygen to survive, and if you soak the soil continuously, your tree roots will die (and so will the tree)
(2) don't forget that dawn redwood is a deciduous tree and needs four seasons. They are cold hardy down to Zone 4 (think southern Minnesota), and I don't think they will survive without a hard cold dormancy. I see them planted here in the landscape in North Carolina, but I don't think they will live further south.