What should I do with merchandise that a street vendor forgot with me on the metro, and I cannot find her, knowing that I have used part of it with the intention of returning its price? And is my use of it forbidden (haram)?

If you cannot reach the owner of the tools, then give their value and the remainder of their merchandise in charity on her behalf. If the merchandise is not suitable for charity, then sell it to someone who will use it lawfully and give its price in charity on her behalf. Ibn Taymiyyah reported that the majority of scholars believe in giving charity from funds whose owner is unknown, such as usurped property, borrowed items, and deposits, and this is what is narrated from the Companions. If you do not remember the price of the tools, then investigate the price of similar items and give that in charity. There is no sin upon you if you used them, believing that they were sold to you, due to your ignorance of the impermissibility of that.