Not sure about the first but my guesses would be different environments (like lush, desert, steppe) or something like that.

2. What is the difference between "attack" and "charge"?
Charge is the bonus given to the unit when it charges and as long as it is in charging state. Unlike in RTW and onwards it is not visible on the unit status but generally speaking afaik if the unit charges (it runs and takes about 3 seconds to get full bonus) it retains the charge bonus as long as it pushes the enemy back...

3. The guide says, that you should deploy spears 4 ranks deep, pikes - 6, archers - 2, swords - 2. What about axes, polearms and cavalry?
Axes and polearms are 2 ranks at all times. It IS mentioned in the guide. :-)

4. What is wedge formation useful for? In my first battles I invariably arranged my cavalry units that way but they didn't perform that great (especially if they had to melee), so I switched for 2-3 ranks deep formation. Yet, I don't know which is more effective.
Formations give different bonuses and penalties:

Keep formation is +2 def, +2 att
Engage at will is no bonus no bonus nor penalty
Wedge is -2 def, +2 att
Skirmish is no bonus nor penalty

As for the usefulness the wedge formation is better for penetrating the enemy formations which is useful against spears to deprive them of the rank bonus. It might be useful if the unit is in particularly deep formation but even then wrapping around the unit with 2-ranks regular is probably still better / more effective.