Direct questions :
What is the delivery charge ?
Do you have any delivery charges? (or "a delivery charge")
What delivery charges are there? (no need for plural)
Have you any charge for delivery? (or "a" charge)
How much does delivery cost?
Are there any delivery charges? (no need for plural)
How much is your delivery cost? (or "What is")
What delivery charges do you have? (no need for plural. You can also say "what delivery charge(s) have you?")
The only one that is truly wrong is #5.
Also:
"Is there a delivery charge (or cost)? " You don't need to say "how much" because the question is implicit.