What are "dmgpart" files and what tools can create, merge, or manage them?
Yes, you're correct. The hdiutil man page has a section on "segmented" files, disk images which are split across multiple files.

Note that simply double-clicking on the first file should automatically mount the entire disk image, taking the others into account with no extra work!
Looking at the old man pages, we can still see segmented disk image support way back in OS X 10.2 Jaguar. (Earlier man pages aren't available there, so it might have existed even earlier.) I'm not sure the extent of support for mounting them in the GUI, but I suspect it was functional back then as well.
I'm not sure about the maximum size of a dmg file, but the man page mentions the limit for sparse images:


  The maximum size of a SPARSE image is 128 petabytes; the maximum for
  SPARSEBUNDLE
                            is just under 8 exabytes (2^63 - 512 bytes minus 1 byte).  The amount of data that
                            can be stored in either type of sparse image is additionally bounded by the
                            filesystem in the image and by any partition map.


A sparse image expands as necessary when files are added to it, in contrast to a disk image which actually takes up as much space as you allocate for it.

Basically, with modern filesystems that support very large files (8EB for HFS+), you're much more likely to hit disk capacity constraints than anything else. It might be more convenient to split your files for network transfers, DVD distribution (as you noticed), and the like.
Disk Utility doesn't provide a GUI for creating these segments, but you can split an image using hdiutil directly from the command line. You specify the base filename and the size of each segment. An example, directly from the man page:


hdiutil segment -segmentSize 10m -o /tmp/aseg 30m.dmg

  
  creates aseg.dmg, aseg.002.dmgpart, and aseg.003.dmgpart.


I also found an application called DMGConverter which has a GUI for segmenting disk images.
You can merge the files using hdiutil convert, for example:

hdiutil convert firstFile.dmg -format UDRO -o output.dmg


which will automatically include the .dmgparts.
See #4.