I fear you still haven't really understood.
A webserver doesn't have a graphical interface (usually). What you have is a command-line interface with nothing but text. Tools like Imagemagick don't work by "opening" a picture and moving the pixels around with your mouse. As Northie already said, they're controlled with text commands like this:
(taken from http://www.imagemagick.org/script/convert.php)
convert input.png -colorspace RGB +sigmoidal-contrast 11.6933 \
-define filter:filter=Sinc -define filter:window=Jinc -define filter:lobes=3 \
-resize 400% -sigmoidal-contrast 11.6933 -colorspace sRGB output.png
So, no, you cannot "open" the pictures on your webserver. You could theoretically issue the Imagemagick commands by hand, but I doubt that any graphic designer is willing to do that.
I see two possibilities:
- You automate the editing process. This is what pretty much every website does. Simple things like cropping, resizing etc. don't require a graphic designer.
- If you do need special editing by a designer, then send it to them by mail or have them download the picture. They edit it on their own PC (with Photoshop or whatever). And then they upload the edited picture again. This can all be done in some convenient web interface.
But please forget this idea of "I'm gonna open some application window on my server, and then my designer will edit the image on the server." A web server is no desktop PC. I you're interested in how a web server normally looks like, put VirtualBox on your computer and install Debian (without a graphical interface). That's how you work: no buttons to click on, no fancy graphics. Just text.