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Lowest specs on late 2011. Will it run okay? http://us.battle.net/support/en/article/diablo-iii-system-requirements

Also, does using your computer slow it down? Like will playing games like Diablo 3 on it make my computer slower? Does browsing the web, playing flash games and watching videos slow your computer down? Mainly, does using your computer slow it down?

You're on integrated graphics, I wouldn't expect miracles, it will probably play fine on low settings.

Define slow down? I'm not sure I understand what you're asking. Having more stuff open at once will eventual bog down any computer once you run out of RAM, but just installing stuff won't.
 
Generally, the more you run at the same time, the slower the computer gets. However, simply having the application installed and not actively running will not slow your computer down.
 
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