How are things now, OP?
This is advice from an adoptee who was adopted from care with siblings at a similar age - if you don't think it will be useful don't read on! I apologise in advance for length.
I think you are right to be aware that there are going to be reasons for the behaviour, even though that doesn't make it easier to deal with. It is pretty horrific going into care. It is terrifying being surrounded by adults who do not know or understand you or love you or like you much (and yes, as much as the adults try to hide it, children know!).
In relation to hours of screaming, giving support and dealing with root cause is good, but if it is related to trauma and being "in brain stem" then in my experience really good things to do are long, long walks, a lot, over a period of many months, trampolining, going for runs, in comfortable cosy clothing. The activity apparently helps reconnect brain and body and levels out hormones and emotions and in my experience works really, really well.
I would try very hard to not walk on egg shells as that will make them feel out of control and also give them the wrong sense of power. In case helpful, with my dc if I say something i know they aren't going to be happy about I say it and then jokingly run for cover as they bellow their fury, to make them laugh (as well as bellow).
Choose your battles as in don't sweat the small stuff...
...but they need to hear "no" when it is reasonable, together with your reasons. DC can handle it as long as they are getting the right emotional support, the latter thing being fundamental. If there is an emotional flood when you say "no" then that (letting out an emotional flood) can be a positive thing, if they are getting the right support. When they shout and scream it may be that the message is "I have lost everything and now you are taking this away from me too" but that is a reason to give support, not to try to avoid the feelings. I also think that certainty and clarity is better - what does "not now" or "yes but later" mean? It is better to be clear so that they know exactly where they stand.
I wrote in another thread that in my case the SW and adoptive parents didn't have a full picture, which meant that there was a huge chasm between what I thought and felt and what the adults around me thought I'd think and feel, and that I didn't have the language and maturity to talk to them about it. I think in relation to this, working on emotional literacy really helps, and the sooner and better you know them well, the easier it will be to help them build foundations. Talk about thoughts and feelings a lot.
In relation to the advice from jellycat much is good but I would be cautious about the limiting choices technique. It was around when I was young and it can be seen by children as punishment, shaming, humiliating. Children need to make choices in order that they learn about themselves and how to handle life and how to recover from making mistakes. I would say it is better to say "no tv" and why and then allow free choices, with help and suggestions in the beginning.
Both my adoptive parents and I faced similar difficulties (I shouted and screamed a lot) and this is advice with hindsight. However, given that everything you do will have an impact, it would be good to chat it all over with a psychologist in real life too.