Is it considered usury or unlawful to agree to purchase gold with someone's money, with the intention of returning the original money if its price decreases, or handing over the gold if its price increases?

The gold purchased by the questioner for her sister is a trust (amanah), and she is not permitted to dispose of it without the permission of her sister, the owner. The questioner is merely an agent, and she is not liable for any loss due to a decrease in the gold's price. If she wishes to buy the gold from her sister, then mutual agreement on the price is necessary. It is permissible for her to offer her sister a higher price to compensate for the loss, and it is valid for her sister to appoint her as an agent for receiving (the payment).