Shipping price entered by customer

For our business, administrator decides what a shipping price is. I need to set up a shipping price as an empty textbox, similar to how product price is setup - 'Customer enters price'. This will allow administrator to enter the the shipping price they want.

Are there any configurations in Nopcommerce to set up shipping price this way? is it possible to change shipping price after Purchase Order was done?

It is possible for the admin to "Edit order totals" on the Info tab of the Order and adjust the "Order shipping" amount, but you will also have to adjust tax (if applicable) and the order total.  Do note that the payment was already processed if using a credit card or similar; if you're using a PO and will bill the customer later, then you should be OK.