To what extent has Chinese culture changed due to the damage it suffered in the last two centuries of foreign invasions and internal corruption? Beyond that, I would also like to know how it has affected modern China and Taiwan.
Was looting and destruction by the Japanese and Europeans widespread?
What physical effect did the Cultural Revolution have, how is it taught now, and what do the Chinese communities think of it?
This is a pretty broad-ranging question...I'll focus on the Cultural Revolution:
Before we talk about how the Cultural Revolution affected historical artifacts and the like, I think we need to quickly touch on one of the core principles that were taught to people at the time. People were basically taught to get rid of the "old" - because the "old" was seen as bourgeoise and not reflective of the "new" China. They were relics of the oppressors, and therefore no longer relevant.
With the mentality that people should strip the "old" to bring in the "new" - many people extrapolated that to mean anything historic had to be purged. Which lead to countless historical artifacts being destroyed or heavily damaged. Now, the Communist Party at the time did not officially sanction this [for instance, there was a document called Several suggestions for the protection of cultural relics and books during the Cultural Revolution that was released in 1967] but such behaviour wasn't actively discouraged, either.
The Red Guards were especially fervent in their desire to "smash the four olds". An example of their - well, dedication - can be found in Beijing Record: A Physical and Political History of Planning Modern Beijing, which quotes a report as noting:
...the red guards demanded the destruction and thorough clearance of all the material culture that has been preserved...but tinged with feudal, reactionary and supersitious colours.
This is an example of what the Red Guards did to one historical site:
On January 26, 1967, the locks of the gate of the Jade Buddha Pavillion inside the Cheungguang Hall [Beihai Park]...was smashed and the precious stones inlaid on the head and robes of the Jade Buddha were chiseled off and taken away...the precious beads in the hands of the Jade Buddha were smashed.
So the after-effects of the Cultural Revolution were that many elements of China's history were lost or heavily damaged.
In terms of:
what do the Chinese communities think of it?
In general, the wide-ranging belief is that the Cultural Revolution was a mistake.
Hello! I study East Asian art history in Berlin. The colonial influence was pretty great at the end of the 19th century. Many western 'expeditions' were made into China while it was still imperial. One big event was the discovery of the Dunhuang manuscripts, a huge scroll library hidden in a cave. Most of these manuscripts were scattered around the globe. Many now in Paris, London and Berlin. Thats just one example from before 1912. What is definitely notable is that, when the political struggles of the early 20th cent. led to civil war and the Chinese Nationalists fled to Taiwan they took with them a good portion of the huge Imperial collection housed in Beijing. These objects were saved from the Cultural Revolution. Another aspect is the extremely good preservations of many Chinese artworks and artifacts in Japan and Korea. A lot of early Japanese and Korean culture came from mainland China through trade and the spread of Buddhism.
Lastly, I have no idea about looting by Japanese soldiers in the 20th century. As for the Europeans, they did destroy quite some stuff during the time of the Unequal treaties, such as the destruction of the Old Summer Palace in 1860 through British and French troops.