The nacelles do not provide power, they house the warp field coils that propel the ship. The warp core provides the power to the warp field coils and the phasers.
Yes! In order to power the lance they had to significantly upgrade the warp core. Since the ship now had more power capacity they were able to add an additional nacelle for faster travel in warp.
I always pictured the phaser lance as a high powered starbase phaser emitter that was never meant for a starship. Due to the large internal capacity and flexibility of the galaxy class they figured out a way which involved major refitting.
([i]just after the outbreak of hostilities with the Klingons) [i]
[i] "You asked me to speak with me Admiral Riker?" "Yes, I want you to take the spare SB phaser emitter and put it on the Enterprise. "