May can bring some iffy weather to the Black Hills, but the Badlands are typically quite warm in the summer, so if you have good weather, May might work well.
It's quite safe in the Badlands if you stay on marked, developed trails. I'm not a back country person, but I know there can be some areas in the Badlands that do have some steep drop offs. This applies to most national parks, however. For photography, I don't think you'd probably have to go very far off the beaten path. There are many overlooks.
I think 1-2 nights should be ample time to capture what you're looking for. For the best photography, you will want to capture sunrises and sunsets, along with daylight photos. The colors change dramatically in different light.
Also, I'm not sure how it is in May, but there are many signs in the Badlands warning visitors of rattlesnakes. I've never seen one there, however. You never can be too careful though.
Enjoy your trip!