How did Tokugawa Japan deal with Christianity and international trade during the sixteenth and seventeenth centuries?
First of all, I believe that the dates that you give here are incorrect. The Tokugawa Shogunate is generally said to have begun in the year 1600. This means that there could have been no Tokugawa policy towards trade or Christianity during the sixteenth century. That said, we can say that the Tokugawa Shogunate generally dealt with Christianity and international trade by making them very difficult, if not impossible.
Between the start of the Tokugawa Era and 1639, contacts with foreigners dwindled. The Tokugawa were trying to greatly reduce the ability of foreigners to influence Japan. For this reason, they put more and more restrictions on foreign trade and they became more hostile towards Christianity. By 1639, there were only three ways to trade with Tokugawa Japan. The first of these was through the islands in the Straits of Tsushima. Trade with Korea was conducted through those islands. The second was through the Ryukyu Islands (the biggest of which is Okinawa). Trade with China was conducted through these islands, which were a vassal domain of the Satsuma daimyo. The most important trading post was in the harbor of Nagasaki, on Kyushu. This was the only place where the Japanese traded with the West. The Dutch, along with some Chinese, were allowed to come to Dejima Island in this harbor and trade there with Japanese who received special permission to enter Dejima. Other foreign trade was banned.
The Tokugawa were also very leery of Christianity. They felt that Christians (who actually made up a greater percentage of Japan’s population in the early 1600s than today) were too numerous and too likely to owe their allegiance to foreigners. Because of this, the Tokugawa tried hard to eradicate Christianity in their realm. The Shimabara Revolt in 1637-8 led to the eradication of essentially all Japanese Christians. After that, all Japanese were required to register at their local Buddhist temples.
Thus, we can see that Tokugawa Japan was essentially isolated. Trade with the outside world was extremely restricted and Christians were persecuted to the point where Christianity essentially ceased to exist in Tokugawa Japan.