China has its own problems. There are obscure family names out there consisting of characters that aren't officially recognized, so computers can't process their actual family names. So those people instead pick the closest alternative officially recognized character instead, purely for the purpose of official documents and appeasing computer systems.
I think in premodern times the Chinese character set was not as centrally regulated as it is now, and therefore there should be quite many instances of independent/local character invention.
many chinese characters consist of combinations of other characters. most common is a combination of two, where one component suggests the meaning, while another hints at the pronunciation.
this shows that new characters can be created not by inventing new strokes, but by simply combining existing characters to convey a new meaning, much like we occasionally do create new words in english by combining existing ones, even though that process in english is not productive, unlike eg. german, where it is quite normal. the difference is that these new words only have one syllable.
with the digitalization the creation of new characters essentially ends. the creation of the simplified chinese character system also pushes against creating new, more complicated characters.
it is going to be interesting to see how that will affect language development. new "words" can still be created by using a sequence of characters, but that means that each character keeps their syllable sound. whereas new compound characters would have a single syllable. so if a new meaning emerges for a syllable, a new character can't be created for it. will this prevent new single-syllable words? or will it lead to multiple characters being pronounced with a single syllable?
Do Chinese characters always have the same pronunciation? In Japanese at least, their Kanji (which are derived from Chinese characters) are often read in entirely different ways in different contexts. For example, 二人 is read as "futari" (two people), but ニ alone is read "ni" and 人 alone is read as "hito".
Mostly yes. In Mandarin, tone can be a bit different depending on context but overall pronunciation doesn't differ that much.
But a major caveat is that pronunciation can be wildly different when spoken with other dialects. Mandarin and Cantonese reading of the same text, even with same meaning, sound entirely different.
that's a good question, i know that there are many characters that share one pronunciation, but i have not come across the reverse. there are different pronunciations in different dialects/languages of course, and maybe some of those get adopted by other dialects (that would make sense for food names for example) but i didn't study chinese, so i really don't know.