Using 15 V laptop charger to power 14.4 V speakers
1) The power into the unit is Power = Voltage x Current: 120V x 0.266A = 32W ca.

Power out of the voltage converter part (max) is 14.4V x 1A = 14.4W
So it is actually giving out less power than is put into it. There are conversion losses and safety design considerations that limits the output power.

2) Yes. It will probably work. Probably without the diode also, but we don't know without more information about the circuit being supplied by the power source. 

The "charging circuit" you are referring to probably doesn't exist in the laptop charger. A laptop charger is most of the time just a power source. The charging regulation is usually done in the computer or in some occasions on a PCB inside the battery.