SYSLOG SERVER/ANALYSIS

In a word: Splunk
it may be overkill, and it takes a little configuration to get going, but it does near-real time analysis and reporting any any number of log files from any number of systems. It's free for small volume (up to 500MB per day), but can run into some serious $$ if you're dealing with lots of logs (e.g. hundreds of GB per day)

LOAD TESTING A WEBSITE?:

There are sites that can do this, but I wouldn't worry about it. Your server is not going to be your limit, it's far more likely to be your network bandwidth. Any Mac Mini is more than capable of saturating most internet links, unless you're in a commercial datacenter with gigabit uplinks to your upstream providers.

I know there is a Mac OS X app that can test and map ones network, complete with graphical maps showing where each machine and server is located in the building

I'm not aware of any app that can build a physical map of your network, since that requires an understanding of building layouts, etc., but logical maps (a list of all the devices on the network, switch ports, etc.) are easy enough. Intermapper is probably a good starting point.