do you know what colour is the hat 是对的吗?

不对
应该说成do you know what colour the hat is ？

Do you know what colour the cat is ?
或者
what colour is the cat,do you think?

宾语从句中应该用陈述语序。
Do you know what colour the hat is ？

错的。应该是Do you know what colour the hat is？ Do you know句式后面的内容要用陈述语序。