Partial answer, once I figured out the general principle - touch random places on the screen, and this app. sometimes produces briefly visible icons that apparently the designers find cooler and easier to use than using the menu button on the phone, or even an always visible icon on the screen....
If I swipe vaguely near the lower left of the camera app's screen (upper right of the device's screen; these positions are always in landscape orientation, whereas my device [and I] prefer portait) I can make a small square image briefly appear; this image contains a thumbnail of the most recent picture I've taken. When tapped, I can see that picture.
I can then side scroll to get to earlier pictures.
If I again touch the lower left of the camera app's window - which can be reoriented back to portrait when in this state - I get a set of 3 icons + a date at the bottom of the window, and one at the upper left. The date appears to be the date the picture was taken.
If I click the first icon from the left, looking like 2 upward pointing diverging arrows, I get a menu:
photo share
amazon send to kindle
bluetooth
email
gmail
picasa
print to retail
text messaging
Then a label" downloaded apps"
I guess I can send the picture to any program I wish, provided it's on the cell phone. How amazingly useful.
The circled arrow - 2nd from the left - talks about a "quick upload" app. which requires me to set up a "default quick upload account" to use it. No clue where it would be uploaded, or what privacy might apply.
The downward pointing arrow - on the far right - offers me the following list
The icon at the upper left that looked like a camera takes me back to picture taking mode
So,
(1) It is possible to see what pictures you have taken.
(2) It is probably possible to get access to the files from other computers, by mailing them to one's gmail account, then downloading the attachments - much more "convenient" than having access to the image files - NOT. (I say probably because I have not yet tried this. Perhaps it will turn out that there are more bugs here, or another layer of impenetrable user interface)
(3) The files themselves are not made available directly to the unfortunate user/owner of the device.