Optimist: Yes, I completely agree with that statement, no writer truly understands a character until they experience that character for themselves. That being said, it's still nice to ask yourself these kinds of questions in case there is an inconsistency or just something downright wrong about your character that usually you'll have to stick to once you've put in a good bit a writing for it. Consider the CSing process like ironing out a shirt whilst blindfolded, except maybe the stakes aren't too high if the shirt is $10 versus the $200 tux jacket you might call the protagonist. 

Toaw: A nice way to work with that might be if she doesn't know this grandfather from any point after her childhood, she might fill in some of the blanks with his storytelling and thus imposing some of the books he read to her onto his dream representation. That could be fun for you to play around with because you could deliberately place blanks where you want and fill them with whatever literature you feel like. 

Rune: I guess that depends on her environment, there are places that are welcoming to that idea, some that encourage it and some that abhor it.

 Xalt: First off, welcome newcomer! Your spinny siggy is fabulous. 

Second; I'm not going to be incredibly lenient with close family members, terrible inconsistencies in personality are hopefully not going to occur. If say, that father you mentioned was accompanied by Mary Poppins as a mother, I'd have to suggest changes to the characters just cause that doesn't make much sense. Unless of course Mary Poppins is secretly repressed and would just fold over at that kind of treatment but... Yeah that darkens the mood a bit too much. Her real life is going to have some grey or maybe even some very dark moments but the cancer is supposed to be the Big Bad here, too much else will distract. 

Third; the protagonist's personality is going to be made after the immediate family is finished, plus whatever else comes within that time period. This means that inconsistencies will be ironed out and instead they'll become flaws that can make this character have a vibrant personality. Because of the number of influences here, she'll likely have many colours of emotion but not to the extent of the Bipolar Disorder that you describe. 

Fourth; I hope you stick around and see for yourself how this is going to work out! If you usually pay this much attention to possible flaws then you should be a valuable member here. 

Fifth; WHY WITH ALL THE NUMBERS!?