I am assuming "mulberry" is a local term since I have never heard of a mulberry guinea before. Please post some pictures so we can see what color it is. You have not said what sex the mulberry and the pied mulberry are. If your pied mulberry is a hen, you could expect to get 50% white and 50% pied by pairing it with the White male. If it is a male, you don't currently have any mixes that will produce white guineas.
The white guinea with his pearl mate will only produce pied guineas which should all be pied pearls if she is a pure pearl without any hidden recessive genes.
Your other pearl hen must have a hidden recessive blue color gene in order to produce lavenders from her pairing with the pied lavender male and should also be capable of producing some pied birds whether they are pied pearls or pied lavenders.
I have no idea what your mulberries would produce since you haven't stated what sex they are and I don't know what color a mulberry is.
Here is a chart of known colors, perhaps you could pick out what color your mulberries are.
http://guineas.com/colorchart/
In the future you can produce more white guineas by mating the white male with a pied hen (yields 1/2 white guineas and 1/2 pied guineas) or mating pied guineas together (yields 1/4 white guineas, 1/2 pied guineas and 1/4 colored guineas).
Good luck.