I have an Asus laptop with the same sandy bridge processor/graphics. The processor scores 6.5 and the GPU scores 5.6 for graphics and 6.2 for gaming graphics in Windows 7 but YMMV.
1. You can take the battery out and run from the AC adapter directly. Just don't let the battery run down too far while in storage, or you'll ruin it. As long as you use it a few times a month on battery its fine to just leave it in.
2. Yes, but RAM is going to be a factor when multitasking. 4GB should be enough but it might not hurt to add more if this laptop can take it since DDR3 is pretty cheap.
3. The HD3000 graphics are pretty good for being integrated as shown by the Windows 7 scores above. This has no HDMI so as long as you don't mind using VGA for your monitor this should be fine. I run dual monitors on mine and it has no issues.
The sandy bridge Asus laptops run pretty cool, a lot better than my old super hot HP. Biggest cons of this laptop are the 4 cell battery which won't last as long on a charge, only 2 USB ports and no HDMI. If you can live with that then its a good deal.
Would using a usb hub to connect a keyboard, mouse, and VGA monitor produce a lag of any kind or slow down how fast you could type, enter info, or switch between programs? That would drive me nuts.
Is only two usb ports a really big deal if you can get a usb hub to add more usb connections? They are pretty cheap.