Your Lavender is not carrying the blue gene as he must have two copies of lavender for it to be showing. So he will breed as black when bred to other colors that are not Lav.
Your white could be carrying a blue gene.. but you cannot get splash from blue cross to black (lav)... only blue and black. You are correct that a splash could come from a blue cross to blue.. but I don't THINK that is the case here. I think that is a white chick... maybe with some leakage.
The yellow chicks are white adults. The blues and blacks will be as they appear. Check out this calculator, the second drop down tab is in English. It doesn't account for leakage..
color calculator
Your offspring when bred back to your sire will give you a percentage of Lav chicks, maybe 25%...
Happy chickeneering!