There are lots of kinds of demons. Some ice-themed, some not. But fiends in general (that is, demons and other lower beings) tend have resistance to fire, if not immunity.
Ikina is not a full half-demon or even close. The ancestry in her is nonspecfic and diluted - when House Gleaves ran the region, they were almost all half-fiend or quarter fiend, and they had no problem..."spreading the love", as it were, amongst their subjects at their whim. So what Ikina has is enough demonic/fiendish blood for it to manifest in her - her parents obviously had some, but not enough, or else she wouldn't have.
She can have cold resistance as well - though that would mean she wouldn't have resistance to acid or electricity (not that there's anything wrong with the trade off). And as for assassins - there are demons and fiends that are good as assasination, as much as there are demons (like the ooze demons) that are good for nothing but being minions, and all kinds of other demons too.
It doesn't ruin the idea, its just her heiritage is not that specific.