No, it is not possible to modify shipping rates

Yes, with HideShip you can create a Shipping method with the Dynamic Shipping Rates but, after the order will be placed, it will need to be shipped manually because it is not connected to a delivery partner.

No, HideShip can only hide or display shipping rates that Shopify already provides. HideShip cannot  edit, or change the cost of shipping methods.
Shopify and your carriers control that part.