MY THOUGHTS because this type of story dynamic REALLY intruiges me and i love it.
we know that all of the past events are definitely set in stone, no matter the route. that is, julian was definitely fed a plague beedle, asra and the apprentice definitely fought over the plague and asra ran away, nadia definitely came to vesuvia to get away from her family and so forth. however, i think some bits in the "present" are up for debate.
things that dont tend to happen in every route: i don't think valerius betrays nadia. the reason that happens, i imagine, is because apprentice is there reaffirming her ability to rule without the courtiers input, and that's a problem for him. so he tried to take nadia out of the picture. following that line of thought with the other 2 currently finished routes, i don't think asra goes searching for his parents because the apprentice was never in the arcana realms with him primarily, and julian never got into the palace to regain his memories. that was perhaps just a short cut in his route.
that being said, clearly events still occur, just in a different way. like in nadia's route, asra is still reuinited with his parents, and as mentioned above, julian does eventually remember things, but perhaps not as much as he did in his own route(ie. his past with the apprentice, it could be up for debate and interpretation).
to answer specific questions as example:
julian does hang in the first three clearly... however, these next 3 are setting up. wildly different. so it's hard to say if it will happen, especially in muriel and lucio's routes. but even knowing his innocence, julian found a way to get himself hung to see the hanged man, so maybe it will continue to happen? that ends up as a set up specifically to reveal the plagues origin, not because julian is thought to have killed lucio.
asra's parents are always imprisoned, but whether they are released or not is what changes. there is no mention of them in nadia's route at the end, but there is in julian's. frankly i just don't know and they clearly weren't dying in the realms, but maybe they eventually are found and released no matter the route?
i would say yes, to nadia's familial conflict. portia always sends the letters to her family, and there's always tension but we simply don't see it because we aren't the one nadia is confiding in. in julian's route, portia would be that person, for example, who may help her through it.
and finally for the canon characters ships! that's probably just for fun for the writers LOL. they get a little side romance to hint at throughout the routes and everyone gets to have someone in the end! ... more or less, at least. there are exceptions like muriel, asra in julian's route, and clearly lucio.
also, i wouldn't really consider them as being "different versions"? just all apart of a wider whole.
i'll take lucio as an example because he's simply the easiest to make this connect to, and also i love lucio 🙇♀️ but it applies to ALL the characters, so keep that in mind please..! i WILL make other examples if needed but this is long enough as is, i think.
i've seen some people argue that lucio is depicted completely different from how he is in the main three routes. possible, but i don't think he is an entirely different "version" of himself. both parts are equally him, he's just handling(.... or not handling at all, rather) the situation differently. one way i see the current lucio from his own route in the another character's route: being excited about the fizzy drink room at the masqurade from asra's route. there's no "evil" there, that's just lucio, having fun like he's wanted to for 3 years. that's the lucio we see now, in his first chapter. but the lucio who throws a whole ass branch at us later in asra's route is still lucio, he's just mad and not handling things well, for good reason really. people aren't that one dimintional irl, so why do they have to be in writing? lucio isn't always this negative and chaos wrecking force. he's also this dumbass who wants to prank, party and love his dogs. since i love using in game reference, here's a scene from asra's route that supports it, because lucio being mentioned at all in this sentence always made me think real hard:
this got long but all in all? all past events are definitely set in stone. all relevant story events always find their way to coming into the story, if not always in the same way they did in the route with which it holds the most weight. also, all of the things that characters do in each route are not special to that route in particular.... if that makes sense LOL. and i cannot stress enough, "all apart of a larger whole" really sums it up. sometimes people simply fail to make to connection or understand how one character can be so different, but again, people and fictional characters can be so multi-dimentional that these sides of themselves occur. think about how different you are with your family versus your close friend group? additionally, just think about how different some things would be in your life if that one person (ie. the apprentice) wasn't in it, influencing it in the slightest way. or large way, like the apprentice does.