Whistling noises from switched-mode power supplies are common and not something to be concerned about (the clue's in the name - the regulation is achieved by means of switching on and off at high frequency, which can cause inductor coils to vibrate like a loudspeaker cone), but it can be annoying.
I'd class the monitor things as 'mildly useful'. The one for our previous meters did at least allow you to access the raw meter reading without moving all the camping kit out of the way. Our current one doesn't have this useful feature (which is a shame, since our provider stopped being able to access the gas meter some time ago), so it just functions as an whole-house instantaneous power meter (not even that, as it insists in reverting to displaying in pounds rather than Watts after a minute or so). The main use for that, as far as I can see, is a way to notice that you've left something on.
As I already have the electricity consumption monitored by means of an Arduino counting the flashes of the meter's blinkenlight, which gives me much more useful time-series data, the monitor gathers dust in a box somewhere.
If you actually want to save electricity, going round with a plug-in power meter to scrutinise individual appliances is usually more useful...
A couple of hours on a set of batteries is piss-poor design, though. Or a fault. (Or perhaps fussiness about NiMH cell voltage?)