Hi,
The shipping method you select in the checkout is common for the whole cart.
and thus, the price you see in the dropdown selector for each shipping method is the price for the whole cart too.
Now I don't know how you configured your shipping methods.
Note that the price of a shipping method is calculated like this:
Price configured in shipping method + (cart total price * percentage configured in shipping method) + ( quantity of products in the cart * Price per product configured in shipping method ) + (for each product: price configured in the "shipping prices" area of the product + (fee configured in the "shipping prices" area of the product * quantity of the product in the cart))
So supposing that you've configured a price of 21$ for the first product in its "shipping prices" area, and a price of 15$ for the second product in its "shipping prices" area, both will add up to 36$ on the checkout if you have both in the cart.
If that's not what you want, then you don't want to use the "shipping prices" area for configuring your shipping methods price.
But I'm not sure what result you want so I'm not sure what to tell you to do.
Your example is not clear since I don't understand why the price of a shipping method should be lower with 2 products in the cart than when you only have one product (remember that the shipping method is for the whole cart).
Now if you want one dropdown of shipping methods for each product in the cart, it's possible. You need to create one warehouse for each product in the System>Warehouse menu, then select the corresponding warehouse in each product's warehouse setting, and finally create a set of shipping methods for each warehouse in the System>Shipping methods menu. On the checkout, the products will be grouped per warehouse, and each group will have its own dropdown with the shipping methods assigned to the warehouse of the group and then you'll see the sum of the selected shipping methods price as the "global shipping price" in the cart.
Regarding the shipping methods price display on the product page, that's because you've activated it in the settings of the shipping price per product plugin via the Joomla plugins manager. So you want to deactivate that setting.