What file types can you convert from a Mac to Windows? What types of files can I change from Mac- to Windows-based file types? What types "just work" on both systems? What types are simply non-transferable or won't work when moved between the OS types?

In particular, I am interested in these three file types: .ess, .app, and .bak.
Your question is very general so here is a general answer:

Document files are all dependant on the software for compatibility, not the operating system. So files like .doc .docx .pdf .txt .rtf etc are all compatible with Windows and Mac. This is the same for files like Photoshop files or Powerpoint files. 

Video files are dependent on the codecs installed on the machine; both Windows and Mac have almost the same codecs installed by default. To view .mov files on a Windows machine you need Quicktime installed. .mp4 or .mpeg files will all work natively.

Image files will all work on both systems. eg .jpeg/.jpg, .tiff/.tif, .gif, .png, etc.

Applications are NOT inter-compatible. You cannot run a .app file on Windows, and you can't run a .exe on a Mac (except in a Windows VM or possibly Wine).

As a general rule of thumb, if you have a file that needs software to open (eg a Keynote presentation) then you would need the same software to open it on the other Operating system (in this case, Windows). Since Keynote is a Mac only product, you won't be able to open it on a Windows machine. In some of these cases, it could be possible to convert the file so it is openable by Windows software; in this case, you'd export the Keynote as a PowerPoint file for use on Windows.