There are not many regulations on what you can grow (the main ones are no illegal drug plants w/o permits, like marijuana... which are regulated)
There are limits on what can be imported into the state, the link to the DOA import list:
http://hawaii.gov/hdoa/Info/doa_importing
There are limitations based on your lot, some will grow just about everything, others not so much...
On our very small town lot, we have: oranges, grapefruit, tangerine, lime, lemon, avocados, biliimbi, moringa, pandan, guava, bananas, papayas, pineapple, lilikois (passionfruit), cherry, coffees, cinnamon, red hibiscus (red zinger tea...), mints, weed cherry tomato, dry taro, cassava, oregano, basil & manilla palm (like betle nut) that we have harvested and grapes, miracle berry, peach, clove, allspice, swamp chestnut( I think that is what it is..) that are still growing - along with some things we have do not use, & some have removed, including mango (too big), kava (not into it) ferns.... and we do use ti for food wraps rarely, mainly for lei...
ETA Was weeding out some vines & forgot all about my Hawaiian pepper & edible ginger... and probably more.... & we do not have chickens that are our own, but there are usually feral chickens hanging out around the gardens...