The part of the United States government that oversees all tariff issues and data is the United States International Trade Commission. They maintain a number of tools for finding specific tariffs on specific products for import, the most detailed being the Harmonized Trade Schedule Reference Tool. You can also download the entire current Harmonized Trade Schedule in pdf. For specific questions, you can contact them here.

Cumulative data on imports and exports and all tariffs are maintained on the USITC Interactive Tariff and Trade DataWeb. You need to register to use this database, but it's free to all. Here you can construct detailed statistical reports of all imports, exports, duties paid, amounts paid by individual countries or groups of countries, both for totals per year and for each commodity.