It will be far easier, and probably cheaper, to just go with three separate systems.

If space is a concern, look into small form factor computer from makers like Shuttle. They're a bit on the pricey side, but the lower volume and higher price means Shuttle can spend more time on quality control than big name vendors.

Another option, strangely enough, is some original Xbox consoles you can probably pick up off ebay. Install a softmod onto them and load on XBMC for Xbox, which includes a rather nice photo viewer. Nice thing about the Xbox, is that it's reasonably small, quiet, and low power. It also has a built in 10/100 network port, so you can stream the images over a network connection or put them on the internal hard drive.

The questions about the independent displays and preventing people from deleting things all kind of depends on what program you use. Generally speaking, Windows is not designed with security in mind. So, since the operating system tends to set the example for all the programs written for it, you won't tend to find many programs that place any kind of real emphasis on security for Windows. They will focus on trying to make it so someone who has an IQ of a severely mentally ******** person can use the computer, which requires assuming that just about any level of decision making is beyond the user's ability. They aren't quite there yet, but you get the basic idea. You don't look to Windows, or programs that run on Windows, if you are looking for any kind of real security.