Looking at the stuff they're describing, it seems these polearms are more like two-handed outgrowths of hammers and axes rather than heavier and more complex spears. My notes above have more to do with spearlike pole arms, which is how I've always envisioned halberds. The scale of the two men fighting, for example, suggests a weapon about 5' long: more maneuverable and less stab-or-downward-chop focused.
I still suspect the blunt part is cleated like that not for any kind of piercing effect but to dimple and better grab a surface (such as a smooth armor plate or a person's clothed shoulder) and the general hookish shape seems specialized for snagging and grabbing. It seems like a tradeoff: if you have a blunt grabber you don't grip as well but it's far less likely to get stuck in the target. If you have a spike grabber it pierces in and grips very well but may become entangled in the equipment and/or flesh of the target.
Still not seeing the benefit of a flat striking surface over a cleaving surface, given that the weight and speed is identical for both but the cleaver strikes a smaller area and thus has a greater ability to split armor and fracture a bone.
One could argue that maybe they didn't know what the hell either and these represent offshoots in the development of polearms. But I'd like to think that men who fight with the gear, talking with men who make the gear, and together all of their lives and their families' lives are at stake in case of invasion, would end up producing a good design. There's probably a lot we're missing.
@loudwhispers: I agree on a lot of your points.
Sideways motions with pole weapons make a lot of sense for blocking purposes - but I just don't see a mass of men all swinging sideways to strike. They would be constantly getting in each others' way. In tight formation (that is, bringing as many men to bear on a segment of facing as possible) it's gotta be all about stabbing and downward chopping.
I've heard of mixed units (the "pike and shot" which evolved into rifles with bayonets for example) but I was talking more about seeing a unit with the polearm equivalent of one guy having an axe, another a sword, another a mace ... to fight side by side most effectively you would need to have weapons that perform the same motions. A great sword would be totally sensible among halberds - again, not making great sweeping arcs unless he's out there in front alone, but stabbing and engaging anyone who gets in too close by holding the sword with hands together or apart.
See here for a drawing of great-sword wielders stepping out from the unit and attacking pikemen. We have, from left to right, an axeman about to chop the head off the second man because there's not much else for his axe to do from that position, the wielder of some kind of stabbing pole arm advancing, and a swordsman making a chopping-down motion to cut pikes.
As for infantry vs. pike, from what I've gathered, pike blocks would try to maneuver around to avoid everything but cavalry. When they must fight another pike block, the pikemen pretty much get stabbed all the time until one unit or the other broke and fled - Swiss pikes were renowned for morale which made them terrifying to fight. You could use your pike to knock other pikes aside, but then your pike is also being knocked aside and you're defending instead of stabbing. When attacked by infantry the infantry generally was able to either break ranks and encircle the pikes, or carefully move in and chop the pikes, resulting in pikemen being forced to swap weapons. The infantry would take casualties of course, it's not foolproof, but in general: pike > cavalry > foot > pike. Missile troops are independent of the cycle, generally faring well at range except against very heavily-armored men (who may still suffer life-threatening injuries) but utterly failing in melee against anyone.
As for armor's protectiveness, I've seen experiments using replica weapons of the right weight and metal consistence against armor of the right construction and metal, and in general,
Leather armor sucks and is useful only against relatively light blunt impacts,
Mail is fine except against a good solid hit, which will still go right through but may be slowed somewhat. Swords can split a mail coat, needle-style arrows jam right through it and regularly inflict lethal-depth wounds. Two layers of heavy, close-knit, riveted mail doesn't quite equal a suit of plate. Butted mail sucks hard against anything except blunt impact, against which it fares as well as riveted mail.
Plate is much better than mail but a solid arrow with a needle-style point will still pierce it and can sometimes inflict an organ-depth wound, axes can still cleave it, spears can still pierce it ... but the effect of the impact is much less severe and it can turn what would otherwise be an organ-depth wound into something survivable, or a bone-chipping wound into a flesh wound.
If you took a strong man with an axe or a spear, and set him up to take his time and really hit a guy in the best field-usable armor of the day, the attack will get through that armor and cause injury. During a long battle, how many times will that good solid hit come in? That's why guys in good armor do still die.