Can you write notes regarding picture
Can you write on the picture to remember what it was about.
iPad 2, iOS 7.0.6, Not sure on that sorry
No. The closest you could come to that with the built-in apps would be to add the photo to a shared stream and invite yourself as a subscriber (see http://help.apple.com/icloud/#/mmc0cd7e99), which would allow you to add a comment to a photo. The comment, however, would only be seen in the shared stream album, it wouldn't be stored as part of the photo file.