Hard wired detectors are generally better. Some have back up power sources should the city power go out. It depends on how much you want to spend. Hard wired detectors are more expensive to install and are generally built better.
A battery-operated smoke detector is one which is not connected to your homes power supply.
If the battery dies the smoke detector sill works, that the biggest advantage to using hard wire.
Any home improvement stores and hardware stores carry a wide variety of battery operated smoke detectors. However rental code requires your landlord to provide a smoke detector in more regions.
If your home smoke detector is tied into your electricity and is equipped with a battery backup you should not need an additional smoke detector. You should insure that the batteries are charged and that the smoke detector is functioning properly at least once a month if not more often.
The battery for the battery backup is weak maybe
You need to make sure that any potential smoke detector is battery operated in case electricity service is interrupted.You also need to remember to change batteries on at least a yearly basis.
Either there is smoke, or the battery is going dead.
The battery in a smoke detector should last a year (though the detector should be checked monthly). The detector works on "trickle" current that is always there. NiCads will lose more current than an alkaline battery from just sitting around - much more. Even a fully charged NiCad will usually not last a year in a smoke detector. Alkaline batteries will easily.
As soon as the detector indicates a low battery, otherwise once per year.
Perhaps a two-stage process. Firstly, gain access to the electrical output in the smoke detector, that drives the noise transducer. Use this (amplified?) to drive the mechanism of your electrically-operated lock.
Normally in a hotel you would not have battery operated smoke alarms. You would have a mains powered fire alarm system connected and networked throughout the hotel building. In this case, heat detectors may be installed as they do not detect smoke...only heat. Although, removing the detector head or disconnecting the detector is illegal and dangerous as it may disconnect the rest of the fire alarms in the hotel and for your electrical safety.
It could be broken, or the battery may be dead.