The IE tab stops the playback if you navigate off for whatever reason, then you need to restart the vid. So, it does stop there, but the file is loaded in the page without graphic & audio engines running per se. The same would roughly apply for pages. I believe its dumping the page, and just holding the specific URL until you go back. That's why it will reload. Like if you typed into the address bar without hitting enter.
If you're worried, hit tabs option, x to close your tabs until they're gone. Nothing running anymore except the one tab you can't close. But if its at new tab screen, no worries, then "back button"" out. FYI, if you hold back for a second, current page will fade back, and this is where you'll see what is running if anything.
The chat, no idea. I would think yes, but not a large amount. It may just send a ping to try to connect, but it shouldn't be overly often. Again if you're worried and see that, switch yourself to offline in status, the lil dude at the bottom of the screen.
I love my 8X too. Got me some Skull Candies, and MAN!! Sick with sound.