What is the ruling on continuing to browse a website displaying nude pictures with the intention of reporting it, especially given that a friend has issued a fatwa permitting looking at a man's 'awrah with his consent?

What your friend told you is incorrect. It is not permissible for a man to look at another man's 'awrah (private parts), whether with or without his consent, due to the Prophet's (peace be upon him) saying: "A man must not look at the 'awrah of another man, nor a woman at the 'awrah of another woman. A man must not lie with another man under one covering, nor a woman with another woman."