It is widely regarded that the early modern age was caused mostly by three factors: the invention of the printing press, the discovery and settlement of america by europeans, and general population growth to have larger workforce.

The thing is, the chinese invented the printing press (with movable letter) 400 years before the europeans did. In europe, the invention is famously attributed to Johannes Gutenberg around 1440 (source), while in China, around 1040 the commoner Bi Sheng already performed printing with movable letters. He created movable type from porcelain. (source). But because the chinese script was so complicated, picking the right letters each time was a chore and so the invention didn't have much impact. Had they used the latin alphabet, picking the right letters would have been significantly easier and they would probably have started the printing revolution instead of the europeans.

Quite possibly. That would also likely have lead to increased literacy and thus to increased economic development. A few centuries later they also had large sea going fleets that could have resulted in an age of discovery lead by China. But instead they chose insularity.

They would have needed a different alphabet that's actually compatible with their language (e.g. bopomofo), but yeah, writing systems that represent phonemes rather than logographies are generally superior. Related: Korea invented an alphabet (hangul) in the middleages, but it only became mainstream in the 19th century. Apparently the elites hated hangul and strongly opposed it, even though it was made by a Korean ruler.

The same problem tripped up several east Asian cultures again, during the computer revolution. Japan got off easy by scrunching kana to half-width and initially ignoring kanji.