have you made up your mind how to cheer up the sick kids?by

have 放在句首,做一般疑问句提问
you 主语
made up 谓语.时态是现在完成时.
your mind 宾语.
到这里,句子的主要成分就全了.改成陈述语气就是：You have made up your mind.
how to cheer up the sick kids 是由 how to 引导的方式状语从句.sick kids 是 cheer up 的宾语.
By singing songs.是省略句.
完整的句子是：I cheer up the sick kids by singsing songs.
所以答语的主语是 I（也就是问句里的那个 you）
by singing songs 是宾语补足语,是用来修饰 sick kids 的