I have not heard this characterization of baptism before. This seems like an anti-Catholic formulation.
The Apostles only taught “one baptism for the forgiveness of sins”. We have received no “water ceremonies” from the Apostles. Neither does the Catholic Church teach any “water ceremonies”.
Yes, this is why they were called Anabaptists, or “again baptizers”. Since the Apostles taught that the first baptism is valid, giving them another when they reached the age of reason/belief was unnecessary.
Yes, this is the main motive for “believers baptism” or anabaptism. Infants and children are baptized through the saving faith of their parents/godparents, just as Jesus was circumcised through the faith of His parents.
They tell Catholics they need to be baptized because they don’t accept their first baptism as valid.
Well, we don’t see the Apostles calling him to be baptized again because he did not have a saving faith. We see them confronting him with his sin which results in repentance.
These things are not mutually exclusive. While it is ideal that we would follow HIs commandments because we love Him, it is not wrong to follow our religion because we were taught to do so, or because itis expected, or because we want to escape the pains of sin. Even if we do what is right to impress others, God is able to work through all of these less than ideal motives to make us grow in grace.