...'died in cancer' is not correct English! we would not use 'in'.
Now I can tell this in Swedish too...
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.
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.
Värfor "i," inte "av"
Both ways work well here.
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.