Why is the item list empty when trading in TF2? as a F2P

As a F2P player, none of your items are tradable, therefore none of them are displayed in the trade dialog.

Limited trading means that you can get items from paid players and trade them to others, but your items from drops aren't available for trading.

While @ardaozkal nailed the direct question here, it is worth noting that you can use your duplicate items without trading them. Most of the weapon drops you have are probably not worth much for trades anyway. So why not use it for crafting? You can create scrap metal with any two items from the same class.

_{(source: steamusercontent.com)}

And then you can use the scrap metal to make items you don't have yet. I see folks scrapping random drops between rounds in team-fortress-2 all of the time.