The easiest way to control who sees Facebook pictures and postings is to set the privacy functions to a desired level. If a person leaves their Facebook account public or semi public, then they are inviting people to view their page. They should not be able to have a public setting and then turn around and investigate who is looking at their account.
Facebook is a private company and the information from the website does not have to be made public. The company does not have to disclose who looks up who on the website. However, it is probably not a good idea to make yourself miserable by Facebook stalking your ex. Even though Facebook stalking sounds creepy, it does not have to become public knowledge nor be banned.
No, the public should not be able to find out who has been searching for them on Facebook. Even though the information gained through these searches may be used for harmful means, it is an invasion of privacy to make the searches people make on Facebook accessible to the public.
It shouldn't be public interest who is looking up who on the Internet. When someone makes an internet page, they are making it for the public to see. For that reason, a person gives up the right to know who looks at it. We shouldn't publicly shame people for doing something as normal as looking up an ex.