displaymacbook proresolutionscreen
I intend to connect my old full HD TV as external display to a mid-2012 MacBook air.
While being "only" 1920×1080, the TV has 42", so each element would look ridiculously large. So I thought about "emulating" it to be, say, 4k, then downscale the signal to the 1080 the TV can handle.
Is there such a possibility?
What's officially "supported" and what's possible don't match. I have a late-2012 rMBP and got 4K out of it at 30Hz.
I took a screenshot as proof:
Just a normal mini-displayport<->displayport cable was used.
More details in my answer here: https://apple.stackexchange.com/a/147765/39878
or on this blog post: http://www.mattburns.co.uk/blog/2014/09/30/running-the-4k-aoc-u2868pqu-and-intel-hd4000-graphics/
This sounds like a hardware failure since all the keys that are not working are around one area. You may have to consider using a USB or Bluetooth keyboard with your MacBook Air. Repairing the keyboard may be expensive.
Best Answer
Assuming you want to extend your desktop and not just mirror it: The Mac does this by default, for more fine grained options go to System Preferences → Screen, a window for the TV will appear, where scaling options is avaliable. For even more options hold down the Alt/Option key while clicking on "Scaled"