Is it permissible to take pictures and information from the internet—such as the fatwas on your website here—for re-publication, and what are the regulations for that?

There is no harm in taking pictures, information, and fatwas from websites and republishing them, provided that credit is given to their originators and theفضل (grace/merit) is attributed to those deserving it. This is similar to dealing with books, newspapers, and magazines. The quotation must be attributed to its owner if it is verbatim, without alteration or addition.