As we saw in SA, ZUN reads physics books too.
In general theory of relativity, all universe is defined by strict equations. Direction of time doesn't matter; so, altering any point of space-time will affect both on past and future of this point. That means, if someone as Remilia would alter future (fate), present and past will be altered as well, though, inside this space-time those changes couldn't be noticed (human's memory would be altered too).
Opposed to that, quantum physics requires to mark special time's direction as "forward". It is needed to work with quantum structures, e. g. Schr?dinger's cat. As you may know, in "past" that cat is in two states at the same time (quantum superposition); while in "future" (assuming we are opening the box "now") it is either fully dead or fully alive. This transformation cannot be done reversly, so, time is asymmetric.
What is really interesting here, in "past" we cannot know in what state cat will be in "future", choice between them is made "now", at the moment when box is opened, and it is made randomly.
Though, if someone like Remilia can predefine that choice, we can speak about "fate". We can predefine or alter future.
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Speaking of death. I think, fairies are not just unusual youkai, they are embodiements of certain aspect of nature. And because of that, they cannot die in normal way; e. g. Star Saphire's death has no meaning as well as star light's death; they are not just strongly connected, they are the same entity, seen from in different ways.
So, that means that Cirno's birth has no meaning too.
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Just thoughts. Magicians use magic consciously, as with a tech, each spell is casted by doing certain chain of actions. Youkai use it subconsciously, they just do magic, without thinking of how to do it. And, as we know, subconsciuosness is much harder to control than yourself's actions - as what we see with youkai, Remilia too.