Does mounting a large disk image require a certain amount of free space on the internal drive?
There certainly isn't the same amount necessary as the DMG, so you sure can mount a 100GB DMG into a file system that has less (there will be trivial consumptions, maybe a few kb, but nothting that you'll notice).

The whole thing works in the way, that the system attaches a file-system driver to the file with the DMG.  The driver will present the DMG file to the system like an "external" drive and perform file requests on behalf of the system on the contents of the file.

Essentially the driver will says to MacOS:  We have a new volume here. So MacOS will then ask the driver.  "Give me a list of content in it", and then the driver examines the inside of the file and presents the list of files organized inside the DMG.  Etc.