Re: Marrying your adopted sister !!?!!??
As far as Islam is concerned, as long as mother of the boy did not breastfed the girl, what she has done, raised this girl as part of her family and now got her (or getting her) married to her son, it is not only acceptable in Islam, but a very virtuous deed for which she would certainly going to get great rewards from Allah on judgement day. Actually, if there is no devious reason behind the marriage, this act of the mother alone (marrying the girl to her son) could lead her to Paradise regardless of many sins she might have.
If you got disturbed by this news, than it only means, your knowledge of Islam is very limited.
Adoption and Inheritance: The way adoption is understood in west or even by some in Pakistan, where adopted child becomes same as biological child, than such adoption is not allowed in Islam. Anyhow, it does not mean, adoption is not allowed in Islam, but that adoption has its own meaning (or modalities).
In Islamic adoption, one cannot rob the child of their own biological identity (adopter cannot give the child his/her name as father or mother … neither child can take any surname he/she wants. Actually, right of biological parents cannot be denied by child or people who adopted the child), neither adoption can deprive (biological) heirs of their inheritance rights (adopted child could not inherit from person adopted). Within the family, child would be treated as na-mahram too (just like cousins are na-mahram). Anyhow, to overcome lack of inheritance for adopted child, person adopted can leave in will whatever he wants to for the adopted child or could even give a part (or whole) of his assets/wealth to adopted child in own lifetime.
Note: One should understand that a child in Islam belongs to biological father, as it is him Allah has given the child, hence no one can change that in obvious or hidden way. Similarly, it is Allah who gives wealth to a person and it does not belong to person who holds the wealth, thus, when a person dies, his/her wealth goes to blood relatives who Allah has named as inheritors and according to the proportion Allah has decided… that is why in Islam, Quranic inheritance law supersedes will of a person. Anyhow, Islam recognises that a person might have responsibility to people who are not heirs, and thus, Islam allows that a person can make will on third of his/her wealth/assets in the name of those who would not inherit. Anyhow, it is not allowed to make will (even for that third wealth/assets allowed) in the name of anyone who would inherit the person, that is to make sure that a person do not use his will to over-write the will of Allah. But, a person can give his wealth/assets to anyone he likes while that person is alive, as Allah has given that person authority over the wealth/asset that person holds while living, and can spend it or give it to anyone he/she wants (while living).