Although not on your list these should not be planted together
Fennel by itself it does not like company but has been ok with ginger, horseradish and gynuura.
cabbages and strawberries
beets and pole beans (bush beans are ok)
beans and onions
onions stunt bean and pea friends: beets, chard, cabbage, carrot, tomato, roses, lettuce pepper, strawberry
Some common sense ones.
vines need all the space or they will run over everything in their path and climb trees
Plants that like a lot of water do not do well next to plants that require very little water
Acidic plants in alkaline soil and vice versa
Dill helps tomatoes when they are young but once it blooms it stunts the tomatoes and perilla around them.
parsley family should not be planted close together, they can cross and apparently it is not pretty.
I like to interplant root crops next to lettuce, they occupy different zones.
Sometimes a tall plant can provide shade for plants that cannot take the summer heat. I plant lettuce and greens under citrus trees in the summer but out in full sun in the cooler months.
High nitrogen feeders like corn require more nitrogen fertilizer and does not do well with root crops (the root crops will make greens instead of roots.
Root vegetables and ornamentals, lavender. and the gray leafed herbs seem to do better in neutral to slightly alkaline soils with bone meal or lime added. Baby's breath does not survive for long in acidic conditions.
greens and heavy nitrogen feeders do better in acidic soils.
Citrus, gardenia, blueberries, prefer acidic soils. They display micronutrient deficiencies in alkaline conditions.
Tomatoes, cucumbers, peppers share some of the same pests, so if there is particularly high pest pressure, rotate to other crops that the pests are not fond of and rotate crops by planting in different beds if you can.
There are several plant famililes. It is best to be able to do at least a 3 year rotation or have 3 beds. It is not always possible to do this because of space and environmental factors. Rotation can also be accomplished by time of planting
Like following corn with beans
Leaving one section planted in a cover crop for 6 weeks use a cover crop over the winter.
Companions can share a bed and rotate together
Follow high nitrogen feeder with a nitrogen scavenger corn with cabbages or nitrogen fixer tomatoes with beans or peas.
Some families do better in the cool season like lettuce, cabbages so they would be followed by the warm season tomato, beans, eggplant, and peppers.
If you have multiple separate beds it would be possible to rotate families from bed to bed.
It helps with minimizing pest pressure and balances out the nutrients that are taken from the soil. All crops do not use nutrients evenly so planting companions or succession crops that use different nutrients helps to keep the nutrient ratios in better balance over the long run.
onions are usually planted in the fall or early Spring.
solanaceae/night shade: tomato, eggplant, pepper, tomatillo
cucurbits: cucumber, squash, melons
cabbage an kale/collards
goosefoot: beets, chard, spinach, orach, quinoa
legumes beans and peas
grasses: corn, wheat, rice, sorghum, rye
asteraceae: composits sunflower, lettuce, dandelion, chichory, chammomile, artichoke, Jerusalem artichoke
rosaceae roes and strawberries
Heather : blueberry and cranberry.
Over time, it gets tweaked, you will find out what works and what doesn't.
Where you have winter, the beds get to rest, mine are planted all the time unless I plant a cover crop or solarize sometime between July and August.
Happy gardening in Hawaii. Gardens are where people grow.