Nothing in your post suggests any proper basis for a change of venue. Moreover, you said the court already denied a request. Judges tend to get annoyed when folks continue to request things after being denied.
Can you not agree with mediation and go in front of the judge?
I don't really understand the question. If the parties were ordered to mediate, then they need to mediate or risk the judge's wrath. If they were not ordered to mediate, then they don't need to do so
How can you get the court to appoint an lawyer for the child in the county in which they live?
You said the court already appointed a lawyer for the child.
Is there any way to get records from CPS about the other children so it shows a pattern?
You can serve a subpoena.
Are family court issues public record?
Family court, yes. But the sorts of records you appear to want may be in juvenile court, and those files are not publicly available.