Yes, you can easily re-order the items that you had previously purchased from a store. Just go to the "Orders" tab and you would be able to see a "Reorder" button on the bottom right for each order in your history.
Click on the button and it will take you directly to the cart from where you can either modify the quantity or even add more items from the store and proceed to checkout to place your order.
Any update on the price and availability of a product reflects at the time of checkout.