Is the marriage of a child of blood with his adopted sister and / or the marriage between a daughter of blood and his adopted brother lawful? And in the case of a man adopted from a family and a woman adopted from another family by the same parents, would the marriage between these two siblings be lawful?
Adoption, by itself, does not create any real relationships and hence does not establish any marriage prohibitions.
وما جعل أدعياءكم أبناءكم ذلكم قولكم بأفواهكم والله يقول الحق وهو يهدي السبيل
And he has not made your adopted sons your [true] sons. That is [merely] your saying by your mouths, but Allah says the truth, and He guides to the [right] way.
However if an adopted child was suckled by the mother, that would create prohibitions. Please refer to "Who are the women that a man is forbidden to marry?".