be busy doing 是不是省略了in 应该是 be busy in doing 还有 上面两个跟be busy with 有什么区别么

如果后面搭配动词，用be busy (in) doing sth ;如果后面搭配名词或代词，用be busy with sth.如：
He's busy doing his homwork.
= He's busy with his homework.

就是没有IN不是省略，有be busy with sth的说法

是的
用法没区别
in强调状态
with强调伴随