I would like to keep track the server activities (e.g last night) within a specific time range, any tool or method recommended? thank you.
the only time-stamped info I can think of would be logs: /var/log/syslog, /var/log/apache2/access.log, and the like. login info would be viewable more readily using
lastlog. $HOME/.bash_history for each user can show non-timestamped data; check the ctime and mtime to see when the inode or data was last updated.
of course, all that stuff is unreliable if anyone besides you has root access; everything is capable of being erased and/or edited.
If your looking on a network level you could try nagios, a nice open source monitoring tool, you can create custom scripts to monitor specific aspects as well check port availability, server uptime etc.. information can be presented in graph and diagram format.
There is a plugin specifically to monitor between certain servers between certain times.