You're correct, I was so focussed on the moving and attacking thing that I incorrectly added that in.
A charge requires/allows movement of 3x movement rate total (24m), each CA is up to 2x movement rate (16m)
So the corrected sequence for 3 CAs. Move (up to 16m), Move (up to 16m), Attack including some movement (up to 8m) as you need to be out of weapon reach of the defender when starting the Attack CA). Alternatively Move (up to 16m), Attack including some movement), Move (up to 16m). Both options cannot have total movement over 24m.
You'd have to stop short on the Move action that puts you into engagement range of the defender or you'd place yourself at a disadvantage versus the non-charger. Alternatively the GM may rule that a charge always requires a total amount of movement of 3x movement rate and allows the Attacker and Defender a CA each at the point of closest approach. These CA would occur in order of weapon reach then Initiative if the reach is the same.
The statement about attacking along the way seems impossible as the Movement in Combat on p 126 seems to state that movement stops when an attack is made. It implies you cannot attack and move. It's also unclear as the word Move is capitalised on p 126 whether this refers to move as in the act of moving (and is capitalised because it's after a colon) or the Combat Action Move.
There seems to be no option to make some movement, strike a blow, then make some more movement in one CA. However I'd see no problem in allowing it to happen if it seemed reasonable at the time.
The following bullet points on p 144 imply the possibility of either the Attack then use movement, or the move then Attack, as part of the same CA.
"• A mounted Adventurer has the choice of continuing (if he has enough movement left to get clear of the enemy’s Weapon Reach) after the Combat Action or stopping. If the charging
Adventurer is on foot, then the defender may choose to let the charger continue; if he does
not, then the charger is now engaged with the Defender and must stop moving.
• If the charging creature continues, the charge only allows a single Combat Action for the
Attacker, their mount (if combat capable) and the Defender during that round, because the
speed of the charging creature carries it clear of the engagement zone."
So some discrepancy between p 144 and 126/7.