I haven’t seen many confirmed “blue lavenders”, but they mostly seem to look like lighter lavenders. Or splashes without the darker spots.
I haven’t heard of that being called pied. Personally, I would probably just call it mottled barred. However, I’m not sure if there’s another shorter name...
Black carrying lavender (known as splits). They wouldn’t look anything different from a black, but if bred to a lavender would get you 50% lavender offspring (and 50% splits that appear black). If splits are bred together, you’d get 25% lavender offspring (and 75% blacks and splits).