Bananas
This video, done by Stephen Brown, covers everything he talked about.
http://www.news-press.com/videonetwork/558094467001/GARDEN-TIP-How-To-Grow-Bananas-
They can be grown in the shade; cannot grow in standing water; space 8 feet apart.
Link downloads a PDF file with more information from Stephen Brown: http://lee.ifas.ufl.edu/Hort/Videos_and_Powerpoints/Fruits_Jamaica.pdf.
Sugarcane
It's a grass! There are commercial varieties and edible/homeowner varieties. Propagate by cutting a mature cane, taking a section with a "band" and planting SIDEWAYS in the ground.
Lots more info here that could keep you busy for days: http://edis.ifas.ufl.edu/topic_book_sugarcane_handbook.
Hog Plum AKA Chickasaw Plum
It's a large, not-so-pretty tree with thousands of delicious fruit. It will get hit with frost, but will come back. Deciduous (drops leaves annually). Link downloads a PDF file with more information from Stephen Brown on hog plums: http://lee.ifas.ufl.edu/Hort/Videos_and_Powerpoints/Fruits_Jamaica.pdf.
A fact sheet from the University of Florida: http://edis.ifas.ufl.edu/m/#publication?id=ST504.
More information from Eat the Weeds: http://www.eattheweeds.com/chickasaw-plum-yum/
