Concept: The Hindu Adoption and Maintenance Act lays down specific conditions for a valid adoption.
Step 1: Check Statement A.
The same child cannot be adopted simultaneously by two or more persons.
\[
A = \text{Correct}
\]
Step 2: Check Statement B.
There must be actual giving and taking of the child in adoption with intention to transfer the child to the adoptive family.
\[
B = \text{Correct}
\]
Step 3: Check Statement C.
Performance of datta homam is not essential for a valid adoption under the Act.
\[
C = \text{Incorrect}
\]
Step 4: Check Statement D.
The child must not have already been adopted.
\[
D = \text{Correct}
\]
Therefore, the correct answer is A, B, D only.