IMac – 2008 MacBook Air connected to a 2011 iMac from DVI to Thunderbolt

Not using the built-in hardware. Only MacBooks with a discrete graphics card can drive a second external display (and even then, only one of the new Thunderbolt displays).

The MacBook Air doesn't have a discrete graphics card, only the Intel HD 3000 one that comes with the CPU. The same applies to the MacBook Pro 13 inch and the 15 inch ones that don't have one of the AMD Radeon graphics cards.

You can drive an external display using a USB connected graphics card. For example I have one of the DisplayLink adapters, which works very well for everything except 3D graphics and full screen video). I use one of these for my second external display on my MacBook Pro 13.

No. Devices connected to the iMac's other ports will still only be accessible by the iMac, not by the connected MacBook.

You can approximate some of the functionality you might get from this by using various software solutions to share your iMac's devices - such as sharing drives over the network, or sharing the mouse and keyboard using Synergy, etc.