When I open the game from the eduke32 menu, I have to redo the settings and worse, my saved games have vanished! How do I get eduke32 to keep these data in mind?

Fisrt off, do this:
Put eduke32.exe in here:
C:\Program Files\GOG.com\Duke Nukem 3D
If you installed to default directory.
If you installed on a 64 bit os, use this location:
C:\Program Files (x86)\GOG.com\Duke Nukem 3D
Double click eduke32.exe, and set everything up how you want it.
Play the game.
Click Esc
Select Save Game, click Enter
Press Enter again in a blank spot.
Type the name that you want to save it as.
Click Enter again.
Exit the game.
Double click eduke32.exe again.
Select Load Game.
Is the game still there?
If so, your settings should have been saved also.
Remember, eduke32 and the Duke Nukem 3D shortcut are not the same, and wont share user options (as far as I know) like key bindings.

Thanks man, it worked. You are better than all the guys at 3d realms combined who can't make a game in 12 years. I mean it. There isn't a way to incorporate my normal Duke saves with the eduke32 one is there?

I think the saved games will automatically port between the 2.
You shouldnt have to do anything.

Nah, they didn't. I had already finished the first episode though, so I just began from the second. Thanks again.