How do I apply a discount for the second and successive items only if the quantity for those items is higher than 1?
You should be able to do this out of the box if you have the Commerce Discount Extra module installed. The offer type to use is Per-quantity product discount (% off). This offer type (and the other per-quantity offer types) was created to support BOGO style offers (buy 1, get 1 free), but we developed them to support any type of discount for any number of matching products.

In your case, you'd set the "Buy #" to 1 and the "Get up to #" to a very high number... whatever you consider reasonable for the quantity you'd expect to discount. This will result in the creation of a new discount line item.

Note that the pattern for matching products will be SKU based or product category based.