If you view a static web page data is only used when you first download it. (i.e. you won't use any additional data if you leave it on your screen for hours). Websites like this one are dynamic, in that they keep sending you data in order to update 'latest posts', so leaving an AB page on your screen (or in a non-visible tab) for hours would add a small amount of data usage to what was initially incurred when first loading the page.
However it's streaming that really uses up data quickly. (Audio streaming, such as when listening to internet radio stations, isn't too bad, but video streaming quickly gobbles up your allowance). An hour of Youtube viewing typically uses around half a Gb.
Sending and receiving mail does, as you suggest, contribute to your data allowance (although the 40Gb might only refer to downloads, so only receiving will count) but, unless you regularly receive hundreds of emails with massive attachments, it's so negligible that you can ignore it. (i.e. your tens of thousands of friends can all send you birthday wishes by email without it having any significant effect on your data usage at all).
Remember that streaming devices other than your computer (such as a Now TV box) all contribute to your data usage. With the increasing popularity of such devices I'm amazed that any ISP still offers data-limited packages. I certainly wouldn't touch one!