Down's symdrome varies in severity. Find a couple of sites that give developmental milestones for babies and children ... your character will be lagging those milestones by a few months to years, or never get there.
Only a few 2 year olds grasp the idea of phones and connect the voice with a real person.
Time out - separating the children - works, but normal children of that age are just getting to the point of connecting actions and consequences. A child with cognitive delays would not be making that connection easily.
I don't know about the only a few 2 year olds comment. My neighbor's daughter talked to grandma when she was two on the phone, and she was always aware of who she was talking to. I have a friend who's daughters used to talk to me on the phone at that age and they knew who I was. I also have another friend who's daughter was little bitty and used to want to call and talk to her grandma. That might have been just wanting to play on the phone, though.
But mostly, think about how little kids are when we train them to use phones. We give them toys when they're teeny tiny and play pretend phone talk to them, so they're well-integrated to the concept. Most people are putting their children on the phone to "talk" even when they can only manage a word or two. Yes, those kids don't usually care and ignore it, but I think at 2 it's perfectly reasonable to expect a child to realize they're talking to their mother on the phone.
Now, as for the question about time outs and the ds, that's going to be a bigger deal. Is she extremely high functioning? I'd also look into specifics of vocabulary building in children. I'm trying to remember now (it's been awhile since I was in school lol), and I seem to remember that the first words learned are simple things like "mommy, daddy, ball," basic nouns. Concepts like "no" and "mine" and stuff come in soon after that. Then you start combining words into two word phrases, so then you'd have things like "my mommy." My first thought is that for a developmentally delayed child, the latter might be a bit much. Then again, she could be high-functioning, in which case it's okay. Same thought with, "Leggo," though. I can see "no" much more easily.
Here's a quick link on normal infant development. Verbs come into the mix kind of late.
As for the time-out...I'd guess that she understands she's being punished or not getting what she wants. It might be more effective to try to emphasize the fact that she hurt her brother instead. I'm not sure on that, but I'm just thinking she
might get what's going on enough to be unhappy with the situation. Or it might be more effective to say, "Look, you made Billy cry! Do you see that, you hurt Billy!" and show the bite mark and Billy crying and then hug the brother to make him feel better and stuff like that. Guilt training? I don't know. That's what I've always used on little bitty ones, and what I've seen a lot of parents do. Trying to link the idea that the behavior hurt someone and build empathy.
I don't actually have much experience with down syndrome, but I studied a lot of this stuff in grad school. It's just been awhile, so don't take my word for it. Just offering an opinion in the hopes that it might help out some.