Question

Don't want to be at home ,don't want to go back to school .

Answer 1

没有错误.如果写成Don't want to be at home,and don't want to go back to school neither.的形式可能更好一点.

有一个小问题就是：这句话没有主语.如果没有上下文的话会造成歧义.英语一般是不能省略主语的.