"Unzip" items so I can use them

Those are bank notes. As you guessed, they can stack higher than the item can without taking multiple spaces in your inventory.
You can exchange them for the items that they represent at any bank.

The other items you have are sets. These function similarly to the bank note.
However, these need to be exchanged by a Grand Exchange Clerk.

What you have is 6 item sets, and 2 noted items. To get the individual items in the set, you must speak to a Grand Exchange clerk at the Grand Exchange in Varrock (north of the west bank). They will have a right click option called "exchange." Using this option, you can get the indivudal items. As for the bank notes, just place them in your bank and withdraw them again.