Can I create a blog where the public can register and upload personal photos?
No. If that was the case then our blogs would be full of unwanted porno and spam.
Either that or place photos from another URL?
Your visitors can provide URLs to images, videos, etc. in comments and you can choose whether or not to approve them http://en.support.wordpress.com/comments/embeds/
P.S. if you set up the blog for anonymous commenting then do be sure to set up full comment moderation ie. "An administrator must always approve the comment" because anonymous commenting is bound to increase the amount of spam your blog will receive.