Day-by-day example of someone in a hospital [shot in the shoulder]

So, I'm creating this interactive game, it's told by texting the characters and emails and stuff. All great fun. But, I recently had one of my characters shot in the shoulder, and his attending physician is relating how he's doing to one of the players. He's stable by now [I think? or at least, not on the edge of death], just got out of surgery last night, but is gonna need therapy to help with his arm, that's all I really know about this situation and that's all I've researched. But the player keeps asking questions about how he's doing each day and I don't really know THAT much about how a hospital works.
Would he be allowed his phone to talk to the player in private? Like, without a nurse or whatnot around?
Would they bug him to find out why he got shot [he can't tell them why, it's... a very long story, but he can't, and he's the only one that knows what happened] or would they just give up and keep treating him?
How long would he be in the hospital to recover, or would he be able to 'escape' in a way if something came up [which I'm planning, maybe if he can't be released in a few week]? Just, yea. It's a bit of an odd question, but I do want to seem like I know a bit about what I'm doing. Anything you can give me, details would be great, make it seem more life-like for the players, ect.

Unless he has been arrested and being detained by the police, he can do whatever he wants. He can leave at any time, even if not medically advisable. He just signs an AMA (against medical advise) waver. He can talk on the phone to whomever he wishes, and nurses could give a rat's *** as to who he talks to.

I can't see needing to stay in the hospital for a week for a shoulder wound. Everything is outpatient these days and as soon as they can kick you out of the hospital they do.