Was a Spearing method or a Chopping method preferred for example?
Thrusting and striking were both used. Which one was preferred would depend on the design of the weapon (overall length of the weapon and shape of the head) and the particular situation.
Historical depictions and combat manuals basically show two ways to wield pole weapons. One way is to grip it toward the butt end. You get a lot of range this way. Thrusting with this grip is very nimble if the head of the weapon is light. Strikes will be slower with a heavy head but they hit insanely hard.
The other way is to hold it toward the middle of the staff. Less reach, but you can quickly attack with both ends. You also have more leverage for takedowns.
Now if the head has protusions, like a halberd does, you can use those to hook or push. The combat manuals show hooking the ankles and neck especially. They also show using the protrusion to push into the opponents weapon and basically catching it.
All this is just scratching the surface, but I hope it helps.
We have dozens of manuals from contemporary fencers like Fiore Dei Liberi and Hans Talhoffer that tell us more or less exactly how they were used by individuals, and more rarely in groups. This is only for a period of time spanning a few hundred years, however. Manuals from before the year 1100 and outside of Europe are beyond my knowledge.
http://www.wiktenauer.com/wiki/Category:Pole_Weapons
http://www.wiktenauer.com/wiki/Category:Staff_Weapons
There are also instructions for several different contexts, such as on a horse, in armor, out of armor, against a sword, etc. etc. These manuals were written across several hundred years of time, so it's interesting to see what changes and what does not.
Fiore structures his polearm writings as a late stage in a sequential progression of competency in arms. He starts with unarmed, then moves on to daggers, then swords, then axe/halberds and spears, and so on. All the while he draws from commonly held guards, grips, attacks, and footwork.
I wait for you without moving in Porta di Ferro, ready to grapple with all of my skill. And this guard can be applied not only in the art of grappling, but also in the art of the Lanza [Spear], the Azza [Poleaxe], the Spada [Sword], and the Daga [Dagger]. -Fiore's grappling
http://www.wiktenauer.com/wiki/Fiore_de%27i_Liberi
Cuts and thrusts were both used in equal measure as appropriate for what you plan to do to your opponent and what you think they might try to do to you. Fiore structures his manual in a building cycle of attacks and defenses. Each section begins with a group of Masters in golden crowns who each demonstrate a guard. A master called "Remedio" (remedy) shows a defensive technique against some basic attack, and then student figures wearing golden garters on their legs demonstrate different variations on the defensive technique. After the student figures there is typically a master called "Contrario" (counter), wearing both crown and garter, who demonstrates how to counter the techniques demonstrated by the master and the students. Sometimes there's another figure who is used to demonstrate even more counters to those. There's a strong understanding of how the weapons interact as physical objects and how to exploit the body mechanics of not only your opponent but also yourself. Fencing masters loved to play with geometry, as well, since it is so important for understanding how weapons and bodies move through 3D space. Later era fencing treatises make an art of it.
Depends on several factors: the size and composition of the unit, its tactical objectives, the type of pole weapon, and same vis a vi the opponent. A tight testudo-type formation might use spears as a unit to push or at least stand off opponents, with concerted, pre-arranged attacks in unison. This would be especially helpful for foot formations against calvary, especially heavy calvary. In a more melee environment, the pole weapon could be used in as many number of ways as the individual tactical need and type of weapon dictated. Some pole arms were used for downward chopping movements in a line to attack / disable an opponent's shield, at times so the man next to you could attack him. Others had hooks to do the same, or to pull riders off horses. So, your question turns on a number of factors, any one of which might go out the window based on immediate need, e.g., a stabbing weapon (spear) being used to achieve an opportunistic slash.
