**what are mosaic kings?**
Mosaics are just aberrant cal kings. I've never bred them, but like most aberrancies they are unpredictable. I'm sure when you breed Mosaic to Mosaic you will get mostly that. But it is not 100% predictable like recessive genes.
**Also, spotted, is that a single recessive gene?**
No, spotted is an aberrancy, not recessive. It is also not 100% predictable, although breeding a spotted to a spotted increases your odds in producing more spotteds.
**Is it just a specialized dot-dash?**
Dot-dash and spotteds came from breeding a striped (dominant gene) to bandeds. Those breedings produce some banded, some stripes, and a lot of in-between (where spotted and dot-dash come from)
I've produced a lot of spotteds and and albino spotteds in the past. IMO, aberrancies are fun to work with, just not predictable. Unfortunately too many people advertise cal kings with incorrect labeling of names and they incorrectly state that a cal king king is het for something that isn't possible. 
Kerby...