As you specifically mention 'college' and 'students', and these questions are sysadmin in nature, I'd suggest you try asking on the sage-edu list.

Most of the items you've asked about are handled by unix commands (look up IP address, update time), and have equivalent modules in Perl. Many of the others have existing tools (nagios, big sister, and openNMS which have been mentioned, and also big brother, From some of your concerns, you should also look at a centralized log host (syslog-ng or the original syslog), mrtg for pretty graphs for management (also helps to visualize cyclical trends), tripwire for looking for signs of tampering, nmap or snort for port mapping, etc.

From the sounds of it -- you've been given a task that you know little about, no budget, and a short deadline. This isn't the type of system that you just drop in -- I've been doing sysadmin work for almost a decade, in the type of environment (higher education with unrealistic expectations, and no money to spend on project that aren't new and flashy) you're describing.

I'm guessing from the way that you've described the problem, that you're relatively new in the sysdamin field, I'd suggest that you step back, and do a little research -- I'd suggest if you're managing any UNIX systems, the purple book, and as you seem keen to do this in Perl, Perl for System Administration. Start small -- get some centralized logging or remote monitoring, then slowly build on it. This is not an overnight project. Depending on the size of your shop, it might very well take a dedicated person a month, as they hound all of the other sysadmins to install the necessary parts on their systems.

And please, please, please don't use SNMP if you don't have to.