Can a person who gives a gift (birthday)to a recepient have the right to take it back once gifted?:
Regarding the property, if it's in your home, no one can take it without a court order or a criminal complaint alleging it was stolen. Since it is unlikely the gp will falsify a police complaint, I wouldn't worry too much about the property.

Generally speaking, the police do not have the right to enter your home or property without a warrant in the majority of cases, Exceptions for responding to call from home and domestic violence.

In the matter of the child, you really need to consult with a local attorney. There are too many variables for anyone to give you specific or accurate advice over the Internet.

Good luck and hang in there.