ooooh, these cookie plates look tempting!
would the Italian rainbow cookies by any chance be cucchidata? Basically a shortbread dough with a filling of glace cherries and figs, rolled up and sliced so that you get small spirals?
They are on my to bake list for this year
as are black & whites.
They're more like petit fours. It's a spongy cake made with almond paste, layered with apricot jam and topped with chocolate.