Hopefully it was just down for the weekend.
Maybe check out http://www.pingdom.com/ for downtime notifications. I use the free package to check on a couple of sites, and while it has a couple of false positives, it's pretty helpful.
I use Pingdom to check both SSL and non-SSL pages (to ensure both HTTP and HTTPS are working). I have also used BrowserMob in the past, which is now a product by Neustar. I believe it can still import Selenium scripts (they may have their own scripting language too) for really custom browser-based tests.
To answer your sub-questions...
I rarely find bugs, because we use a shopping cart that is pretty stable and rarely has problems.
Our site has been down once in about 6 months, for a few minutes (in the middle of the night - probably a server reboot after a security patch or something similar).
We are on a self-hosted solution on a pretty beefy VPS.
do you use a hosting service or have your own? I'm actually using my brothers account at iPage...he wasn't using it so I figured I'd throw my stuff on there. I really want to get this thing working because I can't get myself to work on anything else until it's fixed. When I use GTmetrx or pingdom I am getting good results/scores...seems like the delay is waiting for a response from the server