No homework please, the rules are quite clear and we do not want to be mentionned as "Contract Cheating" site, on the other side we do understand your misfortune, you are the one who will have to show us you work and we will try to guide you or explain your mistakes but do not expect the work be done for you.
That said, lets see what you are up to:
Log when users connect/disconnect can be quite easy but it all depends how the person connects, I usually add a few lines in /etc/profile for that...
Now what about if the user uses ftp, does that count?
and if he connects using remote shell (and so bypasses .profile...)

Good luck