Product price minimum quantity

The min quantity is indeed 0.
The min quantity 0 and 1 have the same meaning because you cannot have a quantity of 0 for a product in the cart. When you set a quantity of 0 for a product the product is removed from the cart automatically.
That's why you don't need to set a minimum quantity of 1.

If you put 0 in the minimum quantity, HikaShop considers that you put 1. That's why, when you put 1 it changes it to 0. There is nothing to change. It works as you want already.

0 can't mean unlimited. How would you have a minimum unlimited quantity ? That would mean that you wouldn't be able to buy the product because you would have to buy an unlimited quantity of it for that, which is not possible since unlimited doesn't have a value and cannot be compared.

There is already a check on the minimum quantity. You cannot have a product with a quantity lower to 1 in the cart in HikaShop. If the user try to set a negative quantity or 0, the product is removed from the cart.

That check is done in the _checkQuantity function of the file administrator/components/com_hikashop/classes/cart.php

I don't understand your suggestion. Having a product with a quantity of 0 in the cart makes no sense to me. If the customer wants 0 times a product, it means that it doesn't want it. Thus, the product is removed from the cart.
If you would explain what you're trying to do, maybe I could understand why you would want someone to be able to order 0 times a product...

Ah ok. If it's just that you don't like to see 0 instead of 1 in the listing of prices of a product I understand. It's easy to change.
Just edit the file price of the view product via the menu Display->Views and add the line:
if(empty($row->price_min_quantity)) $row->price_min_quantity = 1;
after the line:
$row =& $this->element->prices[$i];

And you will have 1 instead of 0. The rest of the system will be the same.

Yes. The quantity is decremented when the order is created. That's to avoid that two persons order the same product and that you run out of stock for an order with the payment is not immediate like with checks or wire transfers or even with echecks on paypal. When the order is cancelled, the stock is incremented so that other customers can buy again the products. There is also a plugin in the commercial editions to cancel automatically orders not confirmed or shipped after a certain period of time.

It's for both editions.

There is no option to change the quantity only when the order is confirmed.