Is it possible for a virus to monitor my Facebook page?

[Mind/Matter]

There are many types of viruses, but two fit what your talking about.

Key loggers track every letter, number or symbol you type and save it into a file that the user could then access. this could be used to access passwords or other secure information

A RAV or Remote Access Virus would allow someone to use a remote viewing program on your computer and see what you see. A RAV however only works if the computer is on and currently open to that page. This would allow someone to see your private information, but would not allow them so see and secure information such as a password if the local input shows *'s as most password boxes do