Try rebooting your iPhone.
Press and hold Home and Power button until the Apple logo appears. Let go of both, as soon as you see it. Your iPhone will power up on it's own.
This won't remove data or change settings, but it might help with your problem.
In the Mail app, you usually wait for the images to load, then you tap and hold them, and a popup will give you the option to save the pictures to Photos.
Does that work?