There are patron saints of step parents but not of step children. However,
there are patron saints of adopted children and I am certain they would be willing to listen to your prayers:
Clotilde
Thomas More
William of Rochester
As per the Patron Saint Index, William of York is a saint but not currently a patron saint.
There is no patron saint of bullying or against bullying.
Yes he is the patron saint of repented thieves.
There is no patron saint of children's health but the Infant of Prague is the patron saint of good health.
The patron saints of unborn children are Saint Joseph and Saint Gerard Majella.
Saint Nicholas of Myra is the patron saint of children, scholars and penitent thieves as well as a number of other causes. For a complete list of his patronages, click on this link.
As per the Patron Saints Index, the patron saints of unborn children are Saint Gerard Majella and Saint Joseph.
I see no specific saint for healing of children. However, St. Brigid of Ireland is considered as the patron saint of healers.
The patron saint against autism is St. Ubaldus Baldassini.
There are patron saints of children or orphans or social workers but no patron saint of child custody.
yes
The patron saint of running water is St. John Nepomucene