Currently I know that it is possible to render only a portion of the scene by Shift+B selecting an area in Camera View.
1)But is it possible to rerender a selection only and keep an old fullscreen render made before?
2)Is it possible to use Copy-Paste between blender image editor and other program for example Photoshop?
In the render window there are 8 slots you choose from the render window header. Change to a new slot for each render. To use in an external editor just save the rendered image from the Image / Save as image menu
As far as I know, the output of the render must (as Richard Marklew alludes to above) be rendered to a file. You can then open the file in Photoshop or any other compatible program.
BTW, it’s well worth the trouble to see just what external file formats your image-processing program is capable of supporting, with or without third-party plugins. Your discoveries just might surprise you, especially if you’re using the full-featured “professional” versions of these programs. (They have a lot of Hollywood customers.)