Can the administrators of Facebook pages and groups see my timeline?

[Steven]

Yes they can. Like a network administrator at a workplace, they can gain access to anything on the systems that they have set up. This is how they review profiles that have been reported for whatever reasons. Some people that managed to hack Facebook to great extents were not prosecuted but actually hired by Facebook, so if they want to see what is happening on your account, by all means they can easily do so. They implemented the security and privacy systems, they know how it works and therefore they know how to bypass those measures.