How to make an admin create/edit post page to look like taxonomy page?

yes, that is a cool idea!

this kind of already happens in the quick edit, if you think about it… you just have to find the code that generates the quick edit and put it on the side like in the layout you showed.

another way to go about it, look into this tutorial, which you may be familiar with:
http://wp.tutsplus.com/tutorials/reusable-custom-meta-boxes-part-1-intro-and-basic-fields/
but try to apply this to the ‘posts page’ instead of ‘create/edit post page’

let me know how it goes and if you run into problems