About (Nodding / Shaking) head (Yes / No).
Does "nod" often come with "yes" and shake come with "no" ?
I'm not quite sure about that,but I think it's often used like so!

ex: He nodded his head yes ,but she shook her head no!

And also , Can I skip "head" from the expression ? to be like: He nods yes , she shakes no !

Question

About (Nodding / Shaking) head (Yes / No).
Does "nod" often come with "yes" and shake come with "no" ?
I'm not quite sure about that,but I think it's often used like so!

ex: He nodded his head yes ,but she shook her head no!

And also , Can I skip "head" from the expression ? to be like: He nods yes , she shakes no !

Answer

So clear! Thank you , Maddy!

Answer

You are correct. Nodding signifies yes/agreement while shaking your head signifies no/disagreement.

Also it is sometimes ok to use nod without the word head, but you never use shake by itself.

She nodded in agreement. She nodded. Both are ok.

He shook is head. This is correct. 
He shook no. This is not quite right.

Hope that was clear enough to be helpful!