OK, I'm with Leia and don't pay too much attention to the double dilutes so I am using this for some education.
Can I assume that each parent carries at least one dilute gene (or more)?
If the possibilities for base colors are black, bay or chestnut, then you must have one red based parent??? And one black based?? And at least one carrying agouti?? How am I doing??? Can you tell us the colors of the sire and dam??
Yes, for a horse to be double dilute, both parents must have cream (one or two copies).
I'm not sure about the rest of your questions, meaning I don't understand what you're asking.
For my girl, sire and dam are both buckskins. Which means she could be any of the three double dilutes We don't know the extension and agouti status of her parents, jsut that they are E_ A_ Crn. Could both be Ee so she could be cremello (double dilute chestnut), could both be Aa so she could be smokey cream (double dilulte black).
I'll give the results tomarrow morning