Well ours is mains, or at least transformer-powered
There are all manner of variations, you can get them proximity activated so they don't display whilst the room is empty, there are remote controls so you could click through manually like some latter-day magic lantern show, really it's just a case of checking through the myriad ads on e-bay and Amazon.
Settle on a display format, I use 16:9 and stick to it for the images you upload, then when it gives up the ghost (they seem to have about a five year-life) get another in the same format. Nobody goes through 2,000 image files re-cropping them to 4:3 individually. You will note that anything shot in portrait rather than landscape is a big disappointment on the frame.
As above, files in the 250-600kb size range are all that is needed for a 10" display, higher resolution is just wasted.
Yes, the intervals are programmable. We have settled on 15 minutes, it gives you time to actually look at the image, rather than a 30-second flash through. Not all offer periods this long. They can be displayed in order, or randomly.
I doubt it's worth spending extra for a super-complex one. It has a simple task to do and the cheap ones do this quite happily. This is why there isn't any need for hyper-resolution displays, you really are looking at the memory, not a photographic exhibition.
Be warned, our is in the same room as the television, we often find ourselves talking through the memories and losing track of the broadcast offering. The cry of "Where was that?" is heard frequently
I add images a couple of times a year; the ones from July's gite holiday are there now. Then it will dredge up an image we haven't seen for years, that's always rewarding.