You would resolve the effect of “engaged” any time a hostile character moves within 5’ of another.
EXAMPLE: Athelstan stands in the middle of a 10’ wide corridor. An ogre is 30’ north of him, and Clovis, a badly wounded mage, is 30’ south of him. The ogre acts first, and charges towards Clovis (60’ away). The ogre cannot reach Clovis because it will become engaged by Athelstan - there is no way to pass him in the corridor without getting within 5’.
If a combatant wants to move through an opponent without stopping to fight him, this is an overrun. In the example above, the ogre could overrun Athelstan to get to Clovis.
A more complex example would be as follows:
EXAMPLE: Athelstan stands in the middle of a 10’ wide corridor. An ogre is 60’ north of him, and Clovis, a badly wounded mage, is 15’ north of him. Athelstan and the ogre act simultaneously. The ogre charges towards Clovis (45’ away from it) and Athelstan moves forward to protect Clovis. Athelstan’s movement rate is 60’ and the ogres is 90’ per round.
The rules as written do not address this situation clearly. When it arises in my own campaigns, I typically will estimate where the two combatants would end up based on their relative movement rates and the distances involved.
So in the example above, I might start by having each combatant move 1/6th of his movement. The ogre would advance 15’, and be 30’ north of Clovis. Athelstan would advance 10’ and be 5’ south of Clovis. Since they weren’t engaged yet, I’d repeat. The ogre would advance another 15’ and be 15’ north of Clovis, and Athelstan would advance another 10’, and be 5’ north of Clovis. Since there’s still no engagement, so I’d repeat, advancing them perhaps 1/24th of their movement. The ogre would advance 3.75’ and Athelstan would advance 2.5’ feet, putting the ogre at 11.25’ north of Clovis and Athelstan at 7.5’ north of Clovis - engaged.
This is more-or-less the method Car Wars uses to resolve phased movement of vehicles. It’s very slow, but precise. I don’t mind doing arithmetic in play for important fights, but many people dislike it. You could use this as a simple rule instead:
Have the simultaneous combatants roll a tie-breaker. Give a +1 bonus to the combatant with the faster movement rate, and another +1 bonus to the combatant who is closer to his desired final position.
Your examples:
Assuming a player or monster have declared retreat prior to initiative but rolls initiative equal to a pursuer. If the retreat movement would take the retreating entity out of the pursuing entity’s charge range but they move simultaneously, does the attack still go through?
If you use my mathematical method, the pursuer would get an attack off. If you use the tie-breaking method, the two combatants would make a tie-breaker. The retreater would get +1 (for faster initiative) but the pursuer would get +1 (because he has less distance to move than the retreater, as he is already in position to attack, e.g. he needn’t move at all to attack).
Assume there is a wounded character, a defending fighter, and an attacking monster. The defending fighting and the monster roll an identical, higher initiative number than the wounded character. If the monster attempts to move to engage the wounded character is the defending fighter also allowed to move to intercept and engage the attacking monster?
If you use the mathematical method, it would be based on the geometry of their positions and their respective movement rates. With the tie-breaking method, you’d roll dice.
Assuming identical initiative, if the movements of a ranged attack target would cause the range increment to change, do we measure the distance according to the target’s original space, end space, or the mean of both?
If you use the mathematical method I’d probably base the range on one-half of the target’s movement rate. If you use the tie-breaking method you’d roll dice.
These sort of situations are by far the most complex and difficult for any initiative system to resolve.