According to the person who actually compiles GIMP on Windows, the problem is related to the GTK+ toolkit. And this makes sense, because GIMP isn't the only linux port to suffer from this annoying problem.
Updating to GIMP 2.8.4 (or higher) will resolve the issue in Single-Window Mode.
Otherwise, you will have to find a third-party program that can automatically maximize windows for you. I am not aware of any free ones but Actual Window Manager will do the job. If it's a bit too pricey, you may be able to get the same functionality from some of their cheaper programs such as Actual Window Guard or Actual Window Minimizer.
In regards to your second question, you can use the following registry script to add the 'Edit with GIMP' option to system image types assuming you have GIMP 2.8 installed to the default directory:
Windows Registry Editor Version 5.00
[HKEY_CLASSES_ROOT\SystemFileAssociations\image\shell\Edit with GIMP]
[HKEY_CLASSES_ROOT\SystemFileAssociations\image\shell\Edit with GIMP\command]
@="\"C:\\Program Files\\GIMP 2\\bin\\gimp-2.8.exe\" \"%1\""
I'm in macOS Mojave 10.4.5 and I had to take Gimp app out of the DMG to make it run. When asked by the system, agree to Open it and it'll work. It won't work if you do it from the .dmg even if you allow to open, it's a matter of permissions. Most probably, you'll want to move it to the Applications folder.
This is an answer to an old question, but it might help people who will come across with it, like I did.
Best Answer
Try UFRaw. You didn't specify the OS in your question but it's available for Windows, Linux and Mac