This is a multiple part question so feel free to answer as few or as many as you like.
*Where in Mediterranean Europe did they trade?
*I am particularly interested in the region that would become what is now Italy before its unification. Did they favor certain states over others? What was their trade relationship with the Papal States? With Venice?
*Where did they trade in North Africa and the Near East? Other than the Barbary Wars I know nothing about it. How much trade happened with the Ottomans?
*What did they normally bring to trade? What did they bring back? How important was the Mediterranean to the overall trade of America at this time?
Thank you in advance.
The largest American export to the Mediterranean was salt cod. There was huge demand for salt cod, both as an inexpensive source of protein, and also in Catholic countries, because the faithful were required to fast from eating meat on Fridays, and salt cod was an inexpensive alternative.
The second largest export from America to the Mediterranean was naval stores; lumber, turpentine, pitch. This was the main export to Mediterranean France, as the French had high tariffs on all salt cod except that from the French fishing fleets and their colonies off Newfoundland of St. Pierre and Miquelon.
Where the Americans traded in the Mediterranean is best evidenced by where they established consulates to help their ships and traders.
The first three consulates in the Mediterranean (set up in the 1780s) were all in Spain, Malaga, Alicante, and Barcelona. Spain was probably the largest trading partner in the Mediterranean for Americans.
It was also somewhat safer to try to trade with Spain, rather than go deeper into the Mediterranean during periods when the Barbary Corsairs were attacking American ships and enslaving American Seamen.
In the 1790s, many more American consulates were established, in Gibraltar, Madrid, Marseilles, Genoa, Leghorn, Rome, Naples, Venice, Trieste, and in Tripoli, Tunis, Algiers and Morocco (these last set up to try to ransom American slaves and negotiate against piracy, more than to enable trade).
In the 1800s, additional consulates were established in Tarragona, the Baleric Islands, Sardinia, Palermo, Messina, Malta, and Smyrna in the Ottoman Empire.
The presence of a consulate indicates that the port had a fairly significant volume of American trade (except the consulates which were more engaged with political rather than trade efforts, such as those in the Barbary States, Madrid, and perhaps Rome).
Spain and Italy were the main trading partners. Outside of these two regions there was only one consulate in Mediterranean France, one in the Ottoman Empire, one in the British Empire (Gibraltar) and one in Malta, (Not counting the Barbary consulates).
Return trade from the Mediterranean to America was not always direct. Although some ships carried Mediterranean goods directly to America, many ships seem to have carried Mediterranean goods to England or the Netherlands, and then traded there for English or Dutch manufactured goods to trade back to America.
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