4-2 and 4-3 are the most stamina efficient maps to farm Blossom Hill petals, but im sticking with 4-5 as im assuming higher level means more chance at getting fancy chests.

so it seems petals do not drop from nation defensive missions yet, therefore each petal is worth 5-6 flower gems value of stamina, depending on either phase 1 or 2 of an event. It will cost more flower gems to refill stamina if you're still low leveled though

Which maps drop blooming birds?

Which maps drop petals? I assume these are the world defense or nation battle maps?

Both can be bought with currency, sun crystals for blooming birds and life crystals for petals. I can farm sun crystals much more easily than life crystals.