...'died in cancer' is not correct English! we would not use 'in'.
Now I can tell this in Swedish too...
Is it unusual in swedish for the letter c be pronounced as k? I think this is the first time i have seen it.
Yes, it's quite unusual.
Kan man också säga "min morfar dog FÖR cancer"?
No. To say "dö för" means "to die for" as in dying for a higher cause (politics, love, etc).
Can you think of any other examples where 'i' is used like this? Is this a common sentence structure for illnesses?
Yes, it works for any illness - or at least I can't think of a counter-example.
So 'i' can also be used as 'root or cause of something' or is it valid in this context only?
I would largely consider it a special case with illnesses.