At what age does a child no longer qualify for a dependent visa in Thailand?

To answer what you are asking, even though for some here you are using the wrong words, the child can no longer qualify for a visa/extension as a dependent to get their visa/extension after they turn 20. At that point they must qualify in some other way in order to get a visa/extension to stay in Thailand. They can no longer do it as a dependent.

Kids under 15 cannot be fined for overstay. Kids under 18 cannot be banned from Thailand.

That said you should have a relevant visa for your child for whatever age to avoid potential issues down the line with them staying here.

They can be a dependant until they are 20.

No kids are covered on another visa. They have a separate visa, although they may be considered dependents.

They start paying all fines from 15 or 16.