It actually depends on what type of poppies you are growing and what time you sow them for the time they will bloom, but to answer one of your questions yes annual poppies will bloom the first year from seed.

Some poppies do fine in some shade they may be a little floppy but they still bloom just fine. As like the tulips they tend to get a little more leggy or floppy when in shade so if your tulips do well in this spot I think the poppies will also.

By the way I think that will be a beautiful display!! I would love to see pictures while everything is in bloom!! Also be sure to save seeds of that mulberry tree, Yumm Yummm!! Do you know what kind of mulberry it is??