It'll take a while to tell, especially depending on breed. Is that a Pekin?
I don't remember what bedding I used, but it was some kind of shavings from
TSC - don't use cedar! Someone else can help you out there, I'm sure. Or ask what they keep theirs on currently at
TSC.
I wouldn't let it swim in a full pool until you know it's healthy and it's got some feathers going on instead of just downy, and even then, it's best to supervise. I didn't let mine really get out of leg-deep water for them for a couple weeks, maybe 6ish?
I can't remember the full name of it, but there is a waterfowl? duck? game bird?? feed that's supposed to be good for them. I'd just keep it on starter feed for a bit until it's got it's feathers in.
There's a toxic list for birds here, but I'd look through the forums for ducks specifically here.
http://www.chickendvm.com/toxic.php Also, wait before giving that - they do need grit to digest it properly, which you can get from feed stores as well.
It depends; I've seen some house ducks do well, but at the end of the day, it is a flock animal. You know your bird best, but I'm sure it'd be much happier with a friend or two.
I wouldn't keep it out at night, especially this time of year (depending on where you are) - it'll be getting colder, especially depending on where you put it and with it being alone; it could get even more stressed outside alone. Do you have a safe garage or somewhere inside to keep it? When it can go outside, there are chicken tractors you could use, but make sure they're predator proof and plenty of room!
Try to get it on duck vitamins ASAP to avoid deficiencies, especially niacin.
http://www.metzerfarms.com/BooksAndEquipment.cfm?affiliate=undef&CustID=22054924&Category=Nutrition I personally used the vitamins (and feed) from here, because it's where I got my birds.
Also, is that blood? Where is it's injury? How are it's droppings?