Native Korean speaker here.
- changed pronunciations so pairs of words are no longer homonyms: NO
- changed spellings so pairs of words are no longer homographs: NO
Spelling of Sino-Korean words are very rigid: with very few exception they are spelled in the way each constituent character (i.e., a Chinese character) is spelled. In most cases pronunciation also matches spelling, modulo some common yet not entirely predictable process - e.g., 성적 is pronounced 성적(seongjeok) when it means "test score 成績", but 성쩍(seongjjeok) when it means "sexual 性的".
In general, I don't think change of orthography results in change of pronunciation, at least not directly. People will just keep talking in the same way they've been talking.
- insertion of word separators: YES but not really relevant
Korean has been written with spaces between words since early 20th century. Newspapers and scholarly articles were full of Chinese characters until 1980s. In Korean, even without word separators it is usually not that hard to tell which part is grammatical suffix, because they frequently have syllables not commonly found in other part of speech. (E.g., if you see 를, it's 99.9% object marker.)
Also, the same problem of parsing occurs regardless of whether one uses Chinese characters or not. A commonly used example is (although a bit nonsensical):
아버지가 방에 들어가신다 Father enters the room.
abeoji(father)-ga(subj) bang(room)-e(into) deureogasinda(enter-honorific-present)
아버지 가방에 들어가신다 Father enters the bag.
abeoji(father) gabang(bag)-e(into) deureogasinda
So, using Chinese characters might enable one to forego spaces in some cases, but since Korean generally uses spaces anyway, it's a moot point.
- use of a synonym to remove ambiguity between homonyms: YES (to a degree)
This is the primary mechanism by which Korean orthography gradually moved out of Chinese characters. But even in this case, the opposition against pure Korean spelling was more political than practical.
Basically, some old-fashioned people were used to writing Chinese characters, and they wanted to keep it, so they argued that loss of Chinese characters will make Korean sentences ambiguous and degrade communication. But the effect was often greatly exaggerated, and in many cases it turns out one can simply use alternate expressions to avoid ambiguity.
It did mean many obscure Sino-Korean words that were hardly ever used in everyday speech became even more obscure. I can't say Korean suffered from that. On the contrary, I think Korean communication actually benefited from forcing writers to write in words that people actually use, instead of lazily copying some combination of Chinese characters from Chinese or Japanese and claiming that it's a new Korean word everybody has to learn. (And of course, if you still want to borrow obscure phrases found deep in classical Chinese literary work, nobody stops you. It's just that people find it less interesting these days.)