Over the past week, I've been trying to learn OpenGL, and do research on porting GZDoom Builder to Mono on GNU/Linux. Obviously, there are hurdles to overcome in porting GZDB to Linux, so this is a quick overview of the issues I've found that need sorting out before GZDB can be used on Linux.
EDIT: WIP GZDoom Builder fork here.
SlimDX
The big elephant in the room. As far as I know, it's used for GZDoom Builder's 2D and 3D rendering, as well as input handling. Obviously, that's going to have to be removed and replaced with an OpenGL renderer. OpenTK looks to be just the thing to do it with. I've been studying OpenGL in hopes of writing an OpenGL renderer for GZDB.
DevIL
There are a bunch of DllImports that reference devil.dll in FileImageLoader. Thankfully, Mono has this handy DllMap feature (part of app.config) which lets you use other equivalent libraries instead of the Windows DLL file. DevIL is available for Linux, so it shouldn't be hard to use DllMaps to make Mono use libIL.so.1 instead of devil.dll. There's also this discussion about dllmaps in .NET Core.
ScintillaNET
This one is used for the SCRIPTS and DIALOGUE editor. Unfortunately, it isn't supported on Mono.
As an alternative, I thought of re-writing the GZDB source code editor using GTK to take advantage of the C# binding for GtkSourceView, but then I'm afraid the whole program would have to be rewritten as a GTK app. I also thought of opening an external text editor such as gedit or Kate, like what happens when you run 'git commit' on Linux, but I don't know if that will work well. I also found an answer on StackOverflow suggesting Mono.TextEditor, but I don't know if it's available outside of MonoDevelop. Another person got a Scintilla component running on Mono using the Eto library, but that may also require rewriting the entire GZDoom Builder UI for another library.
The Visplane Explorer Plugin
Like with DevIL, the Visplane Explorer app is available natively on GNU/Linux. The difference is that the user may have to compile the native code for the VPO plugin themselves.