You can't make a lavender, it is a specific mutant gene. To produce lavenders, you have to acquire either lavenders or birds with the lavender gene.
Yes you can "combine" lavender and blue in the same bird, have not seen any in person, however descriptions often are of a very pale looking bird.
Lavender crossed with a blue will be the same as any blue cross, as lavender is a recessive gene. Meaning lavender will not show up in the cross bird(some people claim it lightens up the blue a tad bit in the "crosses").
White is not a color. It's simply a result of a gene(s) that prevents any color or pattern the bird has from showing up. So a white bird actually can be anything and on top of it there are two completely different common genes for "white chickens"(dominant white and recessive white), so it is impossible to give a simple answer to what would a lavender x white cross will look like.. other than it is extremely unlikely any will be lavender colored.