As long as you have DisplayPort on your machine, the iMac can be used as a display.
Nope, both computers have to be connected via Thunderbolt.
You cannot use your 2011 iMac as a Target Display for your pre-2011 MacBook Air.
What about if you bought apple's thunderbolt cable for £50, and then plugged that into a displayport (not thunderbolt) equipped computer ?
iMac (21.5-inch, Mid 2011) and iMac (27-inch, Mid 2011) support Target Display Mode via Thunderbolt to Thunderbolt cable (2 m) when the source is another Thunderbolt-equipped computer.