By RAW, No.
By RAW Charge Through does what it says it does - lets you Overrun (not Trample) one foe.
It is, however, a very reasonable houserule to allow an animal companion with Charge Through (the Charger archetype gives them the ability to choose it as a feat, useless on a rider as it says 'you' not 'your mount') and the Trample special ability to combine the two and automatically 'Trample' any enemies of the appropriate smaller size between it and it's Charge target.
This is, however, a House Rule, and by RAW does not work.
Let's do a bit of set-up:
Charging
Charging is a special full-round action that allows you to move up to twice your speed and attack during the action. Charging, however, carries tight restrictions on how you can move...
Full-Round Action
A full-round action requires an entire round to complete. Thus, it can't be coupled with a standard or a move action...
Overrun
As a standard action, taken during your move or as part of a charge, you can attempt to overrun your target, moving through its square...
All emphasis mine. Links point to the d20PFSRD
So Overrun may be used it only 2 scenarios:
1. A creature is moving (as per the Move Action), and wishes to pass through another creature's square.
2. A creature wishes to Charge (move double it's Speed in a straight line) and to continue it's charging movement beyond it's target's occupied square.
Steps in the Overrun Process
Scenario (1)
1. A creature (A) takes a Move Action, but it's movement is blocked by another (B) that *does not grant A passage* through it's occupied square. (If granted passage, there is no point in using Overrun.)
2. A declares use of the Overrun combat maneuver, using up their Standard Action for that turn. A rolls a combat maneuver check against B's Combat Maneuver Defence (CMD).
On a successful roll:
3a. A may move through B's square unimpeded. If A is within range of another creature after their move they may not attack it as they have already used their Standard Action.
On a successful roll, 5 or more higher than the B's CMD:
3b. A may move through B's square and B is knocked prone, granting attacks of opportunity to nearby creatures. A may use their attack of opportunity to attack B, using their AoO for that round.[1]
On a failed roll:
3c. A's movement is halted in the previous square in their movement, adjacent to B. They may take any remaining actions (Swift or Free), and their turn ends. They may not attack B, as they have already used their Standard Action attempting to Overrun.
Scenario (2)
1. A declares B the target of a Charge (which is a Full-round action), but wishes to end their movement in a square beyond that occupied by B.
2. As per the specific rules of Overrun, A may use this maneuver as part of a Charge even though Overrun is usually a Standard Action, so A declares use of the Overrun combat maneuver in order to charge through B's occupied square.
On a successful roll:
3a. A may charge through B's square unimpeded. A continues to move in a straight line up to the maximum granted by the Charge. B was declared the target of the Charge, so no further attacks may be made by A against any other creature.
On a successful roll, 5 or more higher than the B's CMD:
3b. A may charge through B's square and B is knocked prone, granting attacks of opportunity to nearby creatures. A may use their attack of opportunity to attack B, using their AoO for that round.[1] A continues to move in a straight line up to the maximum granted by the Charge.
On a failed roll:
3c. A's movement is halted in the previous square in their movement, adjacent to B. They may not take any remaining actions (except Free Actions) because their Full-round Action has failed, and their turn ends.
Bonus Scenario!
A wishes to declare a Charge against creature B, but another creature (C) occupies a square between A and B.
A cannot declare a Charge against B, because of this specific rule from Charging:
You must have a clear path toward the opponent... If any line from your starting space to the ending space passes through a square that blocks movement, slows movement, or contains a creature (even an ally), you can't charge.
- Instead, A decides to declare a charge against C and attempts to Overrun. A's Combat Maneuver Check is successful, so A continues to charge up to their max movement (as granted by the Charge; movement must remain in a straight line). If A ends in a square adjacent to B, A may not attack B as they have used up their actions for this turn; they must wait until the next round and their next turn..
In Sum, to answer your direct questions
1. Yes and No. You don't take a Standard Action to enter their square. There are also two (slightly) different uses of the maneuver, as I've outlined. If charging, the target of the Overrun is also the target of the Charge. Overrun does provoke an AoO unless you have the feat. The other various minor details were also correct. As a side note, I found it odd to describe Overrun's use from the perspective of the target, and have outlined my answer slightly differently.
2. Yes, as per the rule of specificity. It's worth noting that while Overrun does allow you to break your move with a Standard Action, this does mean it uses up your Standard Action and you can't take another until your next turn. (So no attacks after your movement has ended.)
3. No. You don't/can't overrun a creature in order to charge another. The target of the charge is also the target of the overrun. Overrun just allows you to pass through their square; you essentially trade an attack against the creature for mobility on the battlefield. It's also No if moving, as you only have one Standard so you cannot attack after the overrun attempt is made, regardless of success or failure.
4. No. For the same reason as (3), and also for the fact that you cannot target more than one creature with a Charge.
[1]: An attack of opportunity "interrupts" the normal flow of actions in the round. If an attack of opportunity is provoked, immediately resolve the attack of opportunity, then continue with the next character's turn (or complete the current turn, if the attack of opportunity was provoked in the midst of a character's turn). (d20PFSRD)
Best Answer
The way I interpret overrun is that it is just allowing you to do your Overrun at any point during a move/charge, but it takes up your standard action or the "attack" that round during the charge (it doesn't give you some free standard action, as is proven by the existence of Charge Through, which does). The 3.5e Overrun simply said "as a standard action taken during your move", I think the intent of the Pathfinder rule was to just say "during a move, or during a charge, that too."
So you can Overrun someone during a move, or during a charge (double move, +2 to hit, -2 AC). You don't get another standard attack normally, so barring greater overrun or mythic shenanigans, you can't also do a melee attack on them or anyone else - but you can keep on moving past them, which is the special thing this maneuver is trying to give you. You get to bowl over (overrun) someone while on your way to fight someone else with your next round's actions - or, stop and fight them prone, that's fine too, but there's no free attacks/standard actions as part of the base combat maneuver.
Keep in mind the overrun target can choose to get out of the way instead of being overrun, which could let you still attack someone else you were charging at/moving towards.