As much as people like burning swords, there's no way you can make liquid fire stick and give off infinite, significant heat and flames without going off the deep end magic-wise and making the weapon extremely impractical. Hollow catapult and sling ammo is more.. "realistic" of a use
I'd like the substance expanded. It'd need to be stored in airtight containers and even then it'd cool off in a matter of months. The snakes probably shouldn't react to meat laden traps either, it creates an implication that they have to eat meat to sustain themselves and that raises a lot of questions. Actually, I'd like to call to question whether liquid fire actually burns at all. Seems like it'd be a orange, reddish flowing glowy substance the snakes absorb heat with to sustain themselves. There's nothing else in there to eat after all and it'd tie in with the whole underground flora thing. All these things have to get sustenance from somewhere. Treating clothing with the stuff would provide protection against firemen and the massive heat of magma forges. Mind you, magma should probably be made hotter if it's going to be usable for smelting more than tin
For the record, you don't use fire arrows for combat. That rag makes it really hard to actually kill targets. Fire arrows are for lighting buildings and oil slicks on fire