What is the Half Thai Child Visa and what are the requirements to convert a tourist visa to this visa?

You are talking about a 90 day non-O visa based on having a half thai child. IF your child was born out of wedlock (meaning you're not married to the thai mother) you'd have to be granted legal parental rights either thru family court OR thru the local Amphur (if the child is old enough; usually 6 to 8 years old) BEFORE you could use the child for a visa/extension. You would need to have an income of 40K baht a month or 400K baht in a thai bank account in your name only as well to apply for the visa and the yearly extension.

You could convert a tourist visa to a 90 day Non-O visa at your immigration office if you met the requirements and have enough time left on your current stamp. Go to your immigration office and get the hand out listing the required documents needed to apply for the 90 day Non-O visa and year extension.