The reason that china has that internet companies prowess is in large part because foreign companies are blocked from the chinese market, and other barriers. You cant acess google nor facebook in china. I dont think that one can conclude anything about china´s education system from the fact that chinese best know companies are largely internet ones.
Nonsense. This has to be one of the myths the westerners love to sell. Google and Baidu had been competing fiercely in China for years; Google never gained the upper hand. At the time of its exit from the Chinese market, Google had about 20+% search market share while Biadu had about 70%. In one of more recent epic competition between a well-known foreign internet company and Chinese ones, Uber vs. Didi, it was a very fair and fierce fight. Uber's founder focused on China and traveled to China dozens of time a year during the time. It still conceded in the end, and sold Uber China to Didi. There are numerous other examples, such as eBay invested heavily in China and acquired its Chinese competitor eachnet, but in the end still had to concede to Alibaba.
The biggest reason that foreign internet companies lost out to domestic rivals are their lack of agility and adaptability to Chinese market and customers. The major decisions were usually made outside China by foreign executives. China is a giant, complex and fast-movig market; it doesn't usually work that way.
Its very hard for chinese companies to compete with the multinationals that have decades of experience ahead of them. china only really started developing in the last 40 years. For example, geely (AFAIK the largest private chinese car company), only started making cars in 1999. hyundai started making cars in 1968.
It depends upon what market they're competing. For auto industry, where cumulative experiences and decades if not century of technology plus brand are formidable barriers for the Chinese companies. But electric car industry will be different, because the industry and technologies are new, Chinese companies are much better chances. Civilian aircraft industry is another example that it's very challenging for the Chinese companies to compete; it would take a very long time.
But there are some industries of complex technologies that Chinese companies have succeeded. Telecommunication equipment being the most obvious one (no, not because Huawei and ZTE got state subsidies or stole foreign companies' IPs. Those are nonsense). HSR and nuclear power plants are also industries where Chinese companies have succeeded - yes large domestic market plays a big role but at least technology-wise Chinese companies reached parity if not leadership. Other examples include ultra high voltage transmission industry, construction machinery, photovoltaic power generation, wind turbines etc.