Using a 5 cell rechargeable battery may be pushing it a little, it is 6 volts nominal voltage but when fully charged it will be even higher. A 4 cell rechargeable battery would be a safer option.
Since the charger outputs at 300ma, 3300/300 = 11 hours, if the battery is completely discharged. It is safer to under-charge than over-charge your battery, so after you use it i would put it on the charger and check the voltage every hour.
Yes, that should be the only battery you will need. Servos will be happy with the 5 cell pack.