Is there any way to check if a specific user is currently logged in? I know that in the user profile there is a value for "seen", but it isn't always relevant (e.g., user logged out 2 minutes ago, but you see - oh, he has been active 2 minutes ago, so I can think he is still active, I will write to him). If it isn't I will write a feature request.
There isn't, and this wouldn't work well if it were to be implemented.
If a user was reading through a lengthy answer, for instance, they'd be active on the site, but there wouldn't be any way that StackOverflow could know that unless it monitored every mouse movement, page scroll, key press or eye movement a user made.