if a catholic baptizes someone does that make the person catholic?
Yes, The person is also required to inform the nearest Catholic Parish of the Baptism so that it may be recorded in the parish Baptismal Register.
Technically, any baptism that follows the proper form is a Catholic baptism. This is why protestants are not re-baptized when they enter fully into the Catholic Church.
But the question asked is about a person Baptized by a Catholic lay person. They are Catholic and subject to the Catholic Church. A person Baptized by a non-Catholic is not.
Hmmm, I don’t know. If a Catholic baptized an infant in an emergency, wouldn’t the parents still be the appropriate people to choose the child’s religion? Or if it was an adult in an emergency, they might be asked to be baptized by whomever was near, but not have any intention to be Catholic, or even know the person doing the baptizing was Catholic.
As long as the baptism follows the correct form, it is a Catholic baptism and will not be repeated.
No, If an infant or adult is about to die, they should be Baptized even without their consent, but not against their objections. However a Catholic lay person must understand the obligations they are creating if they live, and are required to register the Baptism at the nearest Catholic parish ASAP.