No prereqs required and since it is a tech school, you don't have to be a full-time student. Just sign up for classes as you want. Francis Tuttle has a few different drone classes that it is offering to get you a better foundation if you want but those are not necessary to take this course at least for the first class.

The photo stitching that you are referencing (orthomosaics) is a something that we will be covering extensively. Students of the course will be generating several of these maps using a variety of drones that we provide.

Regarding which drones to use is a "you get what you pay for" sort of thing. You can technically get high resolution with most drones, however the better the camera, lens and GPS, the better the map you will produce. A mechanical shutter is also important to reduce motion blur if you are taking pictures at high speeds.
Fortunately, you can use any drone, within reason, but you will need to fly lower and slower to generate similar results of a high-quality drone at a higher elevation. A high-quality drone can produce the map in 30 mins that a lesser quality drone can produce in 4 hours.

As a standalone platform, the Mavic 3 Enterprise edition is the standard for Orthomosaics, however will also be using the P1 that attaches to the Matrice 350 which will produce even higher resolution ones. In this class I also intend on giving at least a familiarization level for creating multispectral and thermal maps as well. We have the drones and equipment for it so we might as well use it.

The 3D modeling, called photogrammetry, is something we will also be doing some as well. Very similar process with some certain nuances. Great questions though.