If you want a commercial GPS wall clock, Seiko makes several models. I have one - GP502W. They make others too. They are JDM models though, so you'll have to order one from Japan.
In the continental US it can be more convenient to get a clock that syncs to WWV, since it works without an external antenna. WWV is accurate to within 100ns, though you'll have propagation delays depending on your position in the US (I'm 50 miles from the station).
No, it doesn't. You need to set the offset to UTC manually. You also need to set the dates when daylight savings start and end if you live in a place that that uses daylight savings. But it runs on batteries that last for 3 years, so it's very low maintenance.
