I think there is a little bell icon next to the subscription button. If you check it videos send notification too. There is an option somewhere where you can choose which things send you notifications.
They stick around because by default ended streams hang around as a video and so you can watch it after the fact. Maybe they need to update the notifications so it can say "someone was live x hours ago"
For some reason, your website interface is the problem, both on firefox and chrome for me. I know it's the website and not my connection because apps like Orion are able to play your streams at the highest bandwidth setting flawlessly for me.
I've found that third party applications like Orion are far better UI wise than Twitch. The twitch web interface always felt clunky to me. I don't know how they managed to mess up the interface but Orion (a desktop app) plays the video streams far better with no weird lags or stutters.
Give me a break, since when does sophistication count for anything? The most sophisticated /b/tard in existence could write a magnum opus about how he dominates you in every conceivable way, it still wouldn't count for anything based on the verbiage alone.
Make a checkbox and persist it with a cookie, the only use of the cookie would be a binary on/off choice. At the beginning of your script you look at the checkbox's state. If it's off you return out of the sript early, otherwise you run your usual tracking code.
Thus your users wouldn't have to fiddle with disabling javascript just for you(if they even know how to)