Hi,
Well, the fact that when you edit the shipping address, you get a new address is normal since there is no shipping or billing addresses but only addresses for a user.
So when you click to edit the shipping address, which is actually the billing address, the system has to create a new address, and select that new address for the shipping. Otherwise, it would also modify the billing address since they are the same address.
I see however a lot of customization on the address edition on your checkout and see several issues with that as I'm actually not able to choose a shipping address, the billing address fields go over to the shipping address area, the address display has fields but changing them doesn't do anything, etc.
Also, we've added many improvements to the address views of the checkout so updating HikaShop and removing the customizations you had for the address views might help on many of these points.