For example, were they aware of scientific inventions (such as the products of the industrial revolution) or of global political changes (such as the formation of the United States of America not too far east of themselves)?
Trade was not completely shut down. There was trade with China both officially and in the way of Tsushima merchants. After the peace treaty was negotiated with the Choson, trade was slow but steady. The Dutch had a presence that was there since 1605 or so, and even England tried its hand before giving up and focusing on China and India. The Tokugawa shogunate were definitely aware of what the West was doing, as their fear of Christianity even led to restricting Chinese merchants to Deshima along with the Dutch and monitored texts for Christian messages. Although the Early Seventeenth century the Shogun Tsunayoshi even tried limiting trade with China due to the Silver mines drying up, there was still bartering as "fees" were collected to get around the tonnage limits.
Moving to 1720, Yoshimune allowed Dutch books on just about everything, except Christianity. This was the start of Rangaku, or 'Dutch Learning'. Translated works started appearing, along with the Dutch having small factories in Nagasaki that would produce small amounts of Western curiosities. There also was the start of the movement to embrace more Western culture in the 1800's with conservative policies from the Shogunate trying to limit it by arresting people. Then there was Nakahama Manjir who worked on a Western whaling boat, and famously taught English to Fukuzawa Yukichi, one of the more prominent scholars who promoted at least absorbing western technology, and even wrote a piece on adapting 'Western science' to keep with civilization if my memory serves, as he saw how China and Korea were failing to deal with the Western forced treaties and policies. He advocated building up a modern army and adapting technology and to view the Asian continent as the West did, to maintain independence.
On the Executed today site it finds that "During that time, the Japanese reproduced everything from telescopes to automata to steam engines using borrowed texts and dissection of imported goods. Dutch Learning kept Japan abreast scientific advancements even while it maintained its isolation."
This is just a brief answer, hopefully somebody will be able to fill in any spaces in this. Gotta be careful with this though, as it is easy to fall into Euro-centrism with this.
for further reading Fukuzawa, Yukichi. On De-Asianization.
Macfarlane, Alan. Fukuzawa Yukichi and Maruyama Masao: Two Visions of Japan
http://www.executedtoday.com/2010/03/04/1771-green-tea-hag-the-beginning-of-dutch-learning/