I'll try to answer each question in there, let me know if I miss any or you need more info.
What parameters affect the number of casualties?
Multiple things happen upon a nuclear detonation. First is that all Citizens working affected tiles are eliminated. (If they are working a farm tile and it's destroyed, they die too). Your number may have seemed high, but that is not unreasonable because of the size of a thermonuclear device. Every tile is destroyed killed a citizen.
Any units occupying those tiles are also destroyed, all the tile improvements are set to pillaged, any buildings or districts in the tiles are also destroyed and must be repaired to use again, and all tiles are contaminated with fallout.
Fallout damages any unit ending their turn in it by 50 hp. Production is also not applied from any contaminated tiles. This can be cleaned by builders or military engineers but also has a timer before it disappears.
Does the number of casualties change based on what's delivering the
nuke (bombers vs silos vs submarines)?
The number of casualties does not change based on the delivery system. No matter what you use, the impact does not alter. The way you deliver it is simply a means of changing the launch location, which changes where you can strike. If you use bombers/submarines you can usually get closer to enemy territory and bigger cities to target.
The type of nuclear device (thermonuclear vs regular)?
Nuclear devices have a blast radius of 1 and have a range of 12 tiles. They also cost 14 gold per turn to maintain.
Thermonuclear devices have a blast radius of 2 and a range of 15. They cost 16 gold per turn to maintain. The reason these seem to be more devastating is because of the extra blast radius which can kill more citizens working tiles.