For hitting back: Is it with a younger sibling? I have two kids with a big enough age spacing that in a physical fight, it's not a fair fight. My youngest may hit first, but as soon as my eldest retaliates, he really wants out of the fight. Once I get them separated, the discipline piece can wait. If emotions are running high enough that someone is spitting or refusing to listen, then it's not a good time to discuss it. One of the best times I've found to discuss discipline problems is at bedtime, when we're all snuggly in bed together anyway.
For giving a sibling space: I don't see it as one kid's job to give space to the other; I see it as our children's job to share space, and I'll try to engage both children in finding ways to use the space happily. If that's going badly, I will see if I can persuade either kid to leave the area by redirecting to another activity.
Screaming: I try to ignore it. Maybe, depending on how I gauge where she is, I'll encourage her to do it in another room from me, because I'm very sensitive to noise. But really, there's no sense in talking to a child in the moment about it.
For screaming and hitting: It sounds like a lot of this relates to anger. My kids and I have a plan for what we do when they are angry. I have a basket filled with "angry" stuff: a journal with stuff to write and draw with; a cuddly stuffed animal filled with lavendar, a snack, a candle and a lighter (lighting and blowing out candles really helps her take big breaths and most kids like fire, but of course it needs to be done with supervision), bubbles (again good for breath and we'll do it in the kitchen; I'll then get rags to do a quick clean of the floor when everyone is calm), and books (I used to keep books about anger in it, but now I just keep some favorite picture books). It doesn't always work, but we talk over and over about our plan about what to do when we're angry, about what we should keep there to help us calm down... I change up what's in it a little to keep it novel and to reflect ideas my kids have about what they think will help them calm down. I do think it's really, really helped.