So your second question, about the pike, is simple. They were "copies" of the ancient's formations which were updated for the modern battlefield. But they wernt copies per say, because the pike never went away. But it lost a lot of its importance during late Antiquity and the Medieval period. With the rise of Medieval and early Renaissance heavy cavalry, infantry needed a way to defend themselves against this hard-charging knights, and the best answer to a guy on a horse is a long pointy stick. And the Greeks had hit on the best way to employ pikes, which was in a solid pike phalanx. It was only natural that that formation would be emulated by the Renaissance soldiers.

But these formations were not carbon copies of the armies of Alexander. The Renaissance phalanx was famously adopted by the Swiss mercenaries. They used a pike about 10-20ft long, but lacked any form of shield, like both the Hoplites and Phalanges had. Further, the Swiss mixed in other weapons into the Phalanx. While all the men had some kind of sword of defensive weapon, their main focus was usually their pike. So the Swiss mixed in other weapons, like Halberds and long Pole Axes to defend the pikemen from enemies who penetrated the spear wall. But the Swiss rejected many developments, like gunpowder. Their competitor, the Landsknecht, adopted the Swiss style phalanx, but also incorporated gunpowder and a larger variety of weapons, like the famous Zweihander sword.

These formations very obviously emulated the formations of Alexander, but the formations which succeeded them kept the same core idea of the phalanx, but updated it in some interesting ways. The Spanish Tercio eventually replaced the Swiss phalanx as the dominant formation, especially in Germany (where it actually replaced the Landsknecht, the diffrences we already talked about). The Tercio was a solid core of Pikemen and Halberders, surrounded by a layer gunpowder skirmishers. The formation was also strengthened by more skirmishers which formed bastions at the four corners. The Tercio would march around in the pictured formation, and as the Arquebusiers got into range the first line would fire, walk to the rear and reload. Meanwhile the second line would fire, and the whole Tercio would keep moving forward. This difficult maneuver was designed to keep a constant volume of fire against the enemy. When the Pikemen got into charging range, they would move in front of the skirmishers and charge the enemy. On the defensive, the formation would invert, with the pikemen forming squares around their soft and vulnerable musketeers. These Tercios would usually advance in a three unit wedge, though the Austrians prefered a four Tercio diamond. They would feature between 1000 and 3500 (as time progressed, formations usually were reduced in size).

There were multiple problems with the Tercio. First off, It should be apparent that the formations movement and evolutions were very complicated, with a lot of moving parts to gum up a transition from attacking to defending. Even the veterans Spanish army sometimes had a hard time moving from the attack to the defense or vice-versa. Second, pikes have always been better defensively than offensively, and it was the same with the Tercio, which exacerbated the problem by keeping its men in that huge square. So whenever they were engaged in the offensive, only one side of the square was actually in action at any one time. The rest of the men were just kind of hanging out, crushing the guys in the front but not otherwise contributing to the battle. The Tercio was thus extremely wasteful. Further, as was seen at the Battle of Rocroi this crush prevented the front lines from running away. This seems counter intuitive, it should be a virtue that the army has no choice but to attack! But at Rocroi, the Spanish had lost the battle at an early stage, but the discipline and rigidity of the Tercios made them hold their ground until they were annihilated where they stood (actually, this battle is widely regarded the death of the Tercio.)

This formation was killed by its successor, the Pike and Shot formation consisted of muskets and pikes organized into squares formed up into a traditional line. The line alternated, pike then shot then pike, etc., with a unit of both being called a battalion. Battalions were organized into Brigades, which usually featured a consistent number of pikemen and Musketeers. This was an incredibly modern way of organizing your army, because each Battalion, or Brigade, was a standard size and composition. So a commander knew what he was getting, or what he was giving, to another. In combat, the muskets would fire their weapons as normal, but when it came to the melee engagement the Pikemen would rush forward and form a screen in front of the vulnerable musketeers.

This formation was very simple, but flexible and resilient, plus it employed its men more efficiently than the Tercio. But the really neat thing, for us, is that this formation was directly inspired by the Roman Republican Army. During the Dutch Revolt (aka the 80 Years War), the Dutch lacked the manpower required to create a Spanish style army. Instead they created an army which modeled the citizen army of Rome, and even went so far as to mimic the checkerboard pattern of the Roman legions. The concept of Battalions and Brigades was also an attempt to emulate the Centuries and Cohorts of a legion.

The Dutch ideas would be exported to Sweden, where they gestated and were improved by Gustavus Adolphus. Gustavus took his new ideas, and used them to wage a campaign in central Germany which produced decisive success against the Tercios of the Austrian Habsburg Army. (I like that picture because it really shows you how the Austrians liked to employ their Tercios, but it also does an adequate job of showing you the Adolphan army.) However, Adolphus would be killed practicing his new tactics. But by the end of the 30 Years War, his system would be adopted by every major European Power, and would remain in practice until the War of the League of Augsburg, some 50 years later.