OK ok ok, right, thats a bill. Trust me, I took up wars of the roses re-enactment 18 months ago. I have practised with bills for that time. Thats a bill, ie pointy bit at the front, backspike, and curved hook, and as far as i know have always been htat way, think of the uses in a field for cutting with such an implement. Glaives are shorter pole weapons, essentially a heavy sword blade on a stick. They tended to be carried by people with armour, or tinnies as we tend to call them. Generically glaives are pole weapons, pole axes are the more commonly know kind, they have a spike at the bottom, and a big axe head at the top. So you block the top, adn the bottom spike gets you somewhere painful. there is a whole interesting method of fighitng with pole axes adn glaives, but its different with a bill, their hafts are longer, ie about 6 feet. You hold it in two hands, near the end (unless fighting someone with a pole axe) and form a big line, called, a bill line. You all then try to hit the people opposite you, block incoming shots, from hitting you or your mates. Bill lines work as a team, a glaive is more an individual weapon. Halberds, are later period and mroe continental as far as I know, im talking about 15th century england here.
Now, on the bill, see the hook? you can catch other bills hooks or behind peoples knees with it, or tehir arms, wherever you can, pull them forwards, hurt them etc. The spike is obvious enough. But see also the angle between spike and hook? You can use that to push down on an opponents bill, trapping it, so your mates can then kill him.
Bills are quite heavy, galives much less so, as they have less haft. A couple of well founded billmen could take a knight on a horse no trouble. However it takes a bill line to deal with a bunch of knights, because of their armour. You need to hold the knight with one bill, whils the othetrs hit him till hes dead. Remember by this time most knights had plate, but armies were composed muchly of archers, and billmen who jsut wore padded jacks, ie multuiple layers of linen cloth. Good ones were pretty much arrow proof as well. But really, if you meet a good bunch of archers your all goign down, and that includes the guys with the shotguns, since the archers outrange you.
katana? ha, different fighting style, comparing it with this is kind of silly. As far as i know, japanese stuff tended towards lightness, os would it just shattter on the billhead? possibly.
Right as for heavy plate, swords evolved to cope, some varieties got pointier, and longer and stiffer. I dont know how well they worked, but they made them and apaprently used them. I also thought that a ball and cahin had a longer haft than chain, ergo you couldnt hit your own hand. They have an advantage of sorts in that they wrap around the target, or over a shield. Maces were useful, very common in fact, same with axes. It only takes a small dent or two to distort a breatsplate enough so they cant breath properly, and once youve done that, you can capture them and ransom them, or execute them as you wish. That sort of thing would hang from a belt as a side arm.