Can I limit the number of free items per several orders?

If you want a customer to get a free gift only once while making several orders, you can create a coupon and specify '1' in the 'Uses per customer' field during coupon creation on the Rule Information tab:

Important! This will work for registered customers only, so that not logged in users will be able to get free products with each order. To solve this, you can exclude not logged in users from the promo rule.