I have a 21 yr. old friend that passed away leaving a 2 yr. old daughter with no spouse who has legal rights to his belongings his child or his parents

Probably the child, but it will depend upon the probate laws for whichever state or country in which he resided when he died.
More importantly, who is taking care of the child? That person may be the one to file an application with the probate court. The court, in turn, will determine ownership of the property. An adult will be appointed to take care of the property until the child is of age (assuming the child is the proper heir).

What happened to the biological mother? If she is alive, she has rights, whether she was married to him or not.

What happened to the biological mother? If she is alive, she has rights, whether she was married to him or not.

Custodial rights, that is. If she was not married to him when he died, she has no inheritance rights.

And that is what the OP asked.

Any question on law needs to include your general locale as laws vary by area. Without knowing that, we can't know what the governing laws of inheritance area.

As a minor anything the daughter might inherit would probably be held in trust by her custodian.

Scott and AK summed it nicely