Is the house bequeathed to me by my adoptive father considered to be within the one-third limit, or does it exceed it, given that there are other funds for the heirs in the bank?

It is not possible to know whether the bequeathed house is equal to one-third of the estate unless the entire estate is inventoried. If the value of the house does not exceed one-third of the estate, then it is yours. If it exceeds that, then you are only entitled to one-third, and any excess depends on the consent of the heirs. Adoption is forbidden by Islamic law, and it does not establish inheritance or any of the rulings of sonship. The wife of your adoptive father and his daughter are not mahram to you, so it is not permissible for you to be alone with them or to see them without a hijab.