I receive photos as email attachments (or in the body of the email). How can I save them, preferably to the 'photos' app?

Open the email, then click and hold one of the photos until you get a pop up. Then click save images

And in case you didn't know, you can save images from websites too. Same process...press and hold the image.

You can also take screenshots of whatever is showing on your screen. Press and hold the Sleep button...while still holding the Sleep button, press the Home button once. You'll see the screen flash white. That means you took a screenshot. The screenshot will now be in your Photos.