They got stuck, This was especially true of the catholic Japanese. They could still get smuggled back into the country and im sure they did. At that time Japanese were the pirates/ smugglers of East Asia. The Spanish used Japanese Ronin and exiled catholic Japanese as mercenaries. It was to the point that the Vice-roality of Peru allowed only Spaniards and Japanese to openly carry weapons on city streets.

To answer your second question Japanese were always going to the Netherlands with the dutch traders. They would study in Amsterdam for a few years and return. Fukuzawa Yukichi who is on the Japanese 10,000 yen note was the first prominent Japanese to call for teaching English over teaching Dutch to Officials and later school children.

Japanese really got everywhere, the only place I don't know of them traveling would be to Africa, but it would be hard to say with any certainty that they didn't go there ever.

I know that Japanese armies went to Korea several times

During the Tokugawa era? The Japanese invasions of Korea in the 1590s were not Tokugawa since they were ordered by Toyotomi Hideyoshi. The Japanese armies that went to Korea in the later 19th century were also not Tokugawa since the shogunate no longer existed by 1875. There were no Japanese armies in Korea in the 17th, 18th, and early 19th centuries.