My 18 year old daughter had a baby on the 1st and she is disabled by the social security administration for a cognitive disability and she is unmarried, I am the responsible party for her, so who actually has custody and makes legal decisions concerning the baby

You can have guardianship paperwork drawn up by an attorney for you to be the child's guardian.

The girl who had the baby, do you have guardianship over her. Or is she considered a independent adult.

You will need to have the court award you guardianship or custody.
But?>>>> the father of the child would or could have rights to custody of the child also

If the girl who had the baby, is this disability mental, if so was it considered rape when she became pregnant ?

Just not enough info to even quess ( not that it stops me) but still not enough info