My Mother-in-law called the first one a silk tree and the other one reminds me of my empress tree, however my tree has purple flowers.
I just did an image google search on silk tree and what comes up is mimosa, so the first one isn't a silk tree, sorry.
Try red bird of paradise or pride of barbados for the first one.
Yeah, The first one has a similar leaf to the Mimosa but the flower is way off.
Another friend ID'd #1 as Dwarf Poinciana (Caesalpinia pulcherrima).
I think that is correct.