I've noticed that falchions often seem to have these rather peculiar hilts that is like a crossguard where the front quillon bends downwards and the back quillon bends upwards, I'm wondering when these hilts appeared and why they seem to be exclusive to falchions (at least as far as I've seen) and also what the point of the upward-bending back quillon is? I've heard it is to snap the opponent's sword in two but that doesn't seem very plausible.

I don't recall seeing guards like this on swords prior to the middle of the 15th century, before that most falchions seem to have "normal" straight or slightly curved guards just like most double-edged swords.
Though take this as a mere indication, they may have been around earlier than that.

These guards are not limited to falchions either, there are Hangers - in particular the famous examples found at Wakefield from the Wars of the Roses - featuring the same guard and I think I've seen Kriegsmesser or swiss sabres having something similar in some examples though I'm not sure on those last two.
In general it's a style of guard that works best on a single-edged sword, as the downward quillon - basically it's a knuckle-guard - would make using the short-edge on a double-edged sword a bit awkward and difficult - not impossible but not something you'd want for general use.

The upward quillon is unlikely to ever snap a blade, unless you happen to use it against a really flimsy Olympic epee or something like that. It is however highly valuable in catching a blow and trapping the blade for a fraction of a second (or longer if you use it well) which most likely leaves your opponent first undefended and afterwards dead.

Thanks for the information, but what exactly is the difference between a hanger and a falchion? I kinda use falchion as a general term for medieval single-edged swords but perhaps that's incorrect.