final questions :
1. if my MBA outputs 1920x1080 to the 4K monitor, would things seem any sharper on the 4K than it would on a 1080p monitor of the same size?
2. if I get a new MBA 2015 and drive the 4K at 1920x1080, would things seem any sharper on the 4K ?
I think all the menus will seem too small at the native 4K resolution.. so my question is - is there any benefit to a 4K monitor for me since I will run it at a lower resolution anyway? Will things seem sharper?
The 1080p signal coming out of one MacBook is going to be the same as the 1080p signal coming out of any other MacBook, or any other device or computer for that matter (phone, cable box, etc.).
All the monitor sees is a 1080p signal, it doesn't know or care what's generating it.
What the monitor does with it depends on the specific model of monitor. It might display each incoming pixel as a solid block of 2x2 pixels of the same color, in which case there's essentially no difference between a 4K monitor and a 1080p monitor.
Depending on the monitor, it might do "upsampling" which means it will try to "guess" good colors for each pixel to show the input image in a smoother or sharper way (or both).
Remember that upsampling doesn't actually work with any extra image information, so all those intermediate pixel values are just guesses, and they're going to be wrong a lot of the time. It will often blur stuff that should be sharp, or vice versa. This might look fine for TV and movies but I suspect it would look pretty bad for typical computer screen images.
So, if you buy a 4K monitor and send it a 1080p image, I think there are two likely outcomes. Either the image quality is just as good as a 1080p monitor, or it will likely be worse to some degree.