It sounds like you are assuming that your MBA can only display 1136x768 pixels, whether it is on your screen or on the external monitor. At the same time, you are making the exact opposite assumption, that the MBA screen can display more than 1136x768.
So for the first issue, the misconception here is that GPU-->screen-->monitor, when the path it takes is actually GPU-->monitor. It may be best to imagine your MBA has no screen, and instead only has the 2560x1440 iMac display. There is no reason the hardware would tell the monitor to display 1136x768 resolution.
For your second problem, how crisp your screen looks is dependent upon the amount of pixels. When you use switchresx on your MBA, you are telling it to display more pixels than it actually has, so if you made it display 2560x1440, about 75% of the pixels wouldn't show up, just because your screen doesn't have them. This makes it look really bad because whole chunks of the screen are missing. What this does is make everything smaller AND lower resolution.
Hopefully that helps.
Best,
Matt