Which of these things will slow down a mini?

Question

1) Two computers connected to a router, both on, and both connected to the internet.
2) Two computers connected to a KVM switch, both on.
3) Multiple applications running at once on the mini (Mail, Safari, Text Edit, iCal)
4) Multiple instances of Safari open at once, accessing different sites.
s
Mac mini - Intel Core Duo - 1.66/2GB   Mac OS X (10.4.6)  

Answer 1

If you have slow internet access sharing that access through the router will, at times, make one or both computers 'feel' slow while your are browsing but doesn't actually show the computer down.
Both connected via a KVM won't slow the computer down - but warning be careful about what USB peripherals you share via the KVM. My neighbor connected an external hard drive that way and didn't think about the fact that when he switched the KVM it was causing the hard drive to be improperly disconnected.
Running multiple programs will make the computer begin to feel slow because once you've reached the limits of your memory the computer will begin shifting data to the hard drive to allow you to keep launching programs. Since older PPC programs need Rosetta to run and Rosetta is a memory hog, the situation becomes even worse when you are running older programs.
When you open a new window you aren't running another 'instance' of Safari. There's only one running. This won't have any affect other than to draw more data through the internet pipeline which might slow down your internet access until all the pages are loaded.