Q:

Clarity of understanding of the meaning

For example, I want someone doesn't do something then which one will be correct? And also I want him to do this.
Does the first one mean that he will not do this and the second one Doesn't it mean he will do this? What do the others mean?

I ask you not to do this, do not ask him.
I ask you not to do this, ask him.
I ask you to do this, do not ask him.
I ask you not to do this, ask him.

A:

None of those expressions is idiomatic English.
I want someone doesn't do something would have to be "I don't want someone to do something"
If you were requesting another person to pass on the message, you could say "I ask you to ask him not to do it." 

