How setting price after checking user order(request)

Hi,

What you could do it to configure a payment method which would be "collect on delivery" with the name you want like "payment will be done after your order is reviewed". Make sure its order is the first one and remove the "payment" view from the checkout workflow in the HikaShop configuration. That, way your customers won't have to pay during the checkout process.
And set a price of 0 to the products with a translation override of the "Fee" word to say something similar.
Then, when you receive the order, you can edit it in your backend and set the prices you want and change the payment method to another one. Then, change the status of the order to a status "waiting for payment" that you would have created in the menu System>Order statuses. Make sure that only this status is enabled under the "unpaid" column there so that the customer will get a payment link in the notification email when you change the status of the order to this status.