Analytics is Google's statistics service. It tracks the number of visitors, where they're from, how they got to the site, and a whole bunch of other stuff. Disabling javascript would keep it from doing its thing, but there are aspects of the Auctiva site that require javascript too, so that may not be an option. Regardless, it's unlikely that Google is causing the slow down.
Google APIs is a service that hosts commonly used javascript libraries for developers on Google's infastructure. Why it and Analytics are showing up in the status bar when the site is being slow, I'm not quite geeky enough to give a great answer, other than I'm sure Google isn't causing the slow down. As a web designer, I've got quite a bit of geek in me, but sorry to say not enough for giving a clearer answer to this one.
As for IE 8, I'm all about Firefox myself, but if you want to give it a shot, probably wait until it's out of beta.