This sounds odd to my AE ears.If the supposition is right, I can take it into the below.
"I can't do with all this loud music."
I don't believe this is what it's saying at all.= All this loud music presents / works / has an effect against me in trying to do.
Actually, this sounds quite good.But in the next, it seems to be not smoothly..
"The boys didn't know what to do with themselves when school ended."
You are almost right with that - the idea is correct, but it is not colloquial. In BE it would be colloquial to say "I can't be doing with all this loud music""I can't do with all this loud music."
That is exactly right. It means that the boys could not decide what they were going to do to keep themselves occupied now that school had ended."The boys didn't know what to do with themselves when school ended."
You are correct. The British have long been keen on understatement. It is, unfortunately, a good way of being misunderstood (the Falklands War may well have been, in part, the result of understatement). There is a more forceful way of understating o) "I could really do without that" meaning, for example, "I am extremely upset about that". In the case of Google's Buzz it does not mean "they were annoyed", it means that Buzz was a potentially catastrophic business decision which caused a huge amount of anger among Googlemail users.Yes, bepleased, could do with and could do without are related, if that's what you're asking.
To me, they're both understatements. I'm saying that with some hesitation as no one mentioned it so far.
I think "I wouldn't mind having a cup of tea" would be a near synonym for the former, meaning I'd like a cup of tea.
As for could do without, it seems to mean Google would have been no worse off if it hadn't happened, but what it really means is that they were fairly annoyed.