Welcome. For beginners you started big.
You can harvest greens like lettuce, chard and kale from thumb size on the lettuce (harvest outer leaves), kale and chard are cut and come again so you can continue to harvest leaves as soon as they are big enough and you could even cut the whole top off and it will grow back again for a second harvest. Lettuce does reach a point where you have to harvest 30-50 days. Swiss chard and kale can be harvested longer.
Peppers can be picked at any stage from green to red. Red peppers are sweeter and if they are hot peppers they also get hotter as they turn red. Pick them anytime you want to but I would wait until they reach full size.
Cucumbers should be picked when they are 7-9 inches long depending on the variety. You don't want them to be too fat or seedy. I prefer the burpless, Japanese or English cucumbers as they are not bitter or gassy. Trellis them up to keep the cukes straight. We bag the young fruit to keep cucumber worms and fruit flies from stinging them. The bag can be removed once the cukes are 4 inches long and the skins hardens.
Carrots- I like the nantes and Nelson varieties. Carrots are usually fall crops they don't like heat and will turn bitter and the cores get fibrous if they are old. They can be harvested around 70 days. They don't like temps higher than the 70's.
I cage tomatoes since I don't like to prune and it is easier just to push the vines inside the cage. Tomatoes can get to be over 8 ft tall so I like to use a CRW cage at least 7ft tall. Birds are a problem as they like to eat the tomatoes as soon as the red starts to show so I have to pick them at first blush. After they get a taste for them they will go after any large tomato even when it is green. I have to use bird netting to keep them out and I use plastic fencing on the bottom since my bird netting does not reach the ground and the birds will go under the netting to get the fruit. Of course that does not stop the slugs and snails so I have to bait too.
Pests attack weak plants and they explode when there is a lot of new growth around. Keeping plants healthy and well spaced makes them poorer targets. Don't use too much fertilizer, it triggers uncontrolled growth and attracts more aphids.
I hardly have any real issues with aphids except on gardenia and the citrus and that is mainly because the ants like to nest near certain plants. I usually control them with ant bait placed at the base of these plants. I replace the baits whenever I see ants or sooty mold on the plants. I don't usually spray for the aphids or scale. I will prune and space plants to maximize air circulation and when I water I use the jet spray on any of the young leaves if I see aphids on them and if I do that every day, it takes care of them.
I have a diverse garden. I have plants that flower and provide nectar and pollen year round that keeps the beneficial insects around. It rains often enough that the bees and other insects can lap off water off the leaves so I don't have to have a water source for them. You can create habitat for beneficial insects by
1. Provide water in the dry season, either wet the leaves early in the morning or place a saucer filled with pebbles and some water out in the garden. Insects like butterflies and bees need a landing spot and the pebbles provide that and they can lap up the water between the stones.
2. Provide habitat: Bare ground for ground nesting bees and wasps. Shrubs and trees provide shelter and homes. You can make artificial nests for solitary bees, bats houses, and bird houses to attract insect eating birds. Hollow logs, crocks, PVC pipes half burried under shrubs and a small pond with fish makes a good home for toads. Geckos eat a lot of beetles, mosquitoes, ants, flying insects, and worms. Birds eat worms, grasshoppers, frogs, geckos,and locusts. My birds will eat slugs and snails only after I kill them and smash the shells open, they like to eat papaya and my seeds so I have to cover the seeds to protect them. Gotta take the good with the bad.
3. Plant flowers that provide pollen and nectar. Choose ones that bloom a long time and have something in bloom for most of the year. Some of these can be invasive so choose the ones you can control and bloom the longest for you. Achillea, fennel, dill, basil in bloom, sage in bloom, sunflowers (the kind with seeds), single flowered marigolds, cosmos, zinnia, daisies, alyssum, penta, false heather, poppy, angelica, caraway, Queen Anne's lace (any parsley relative in bloom), coriander, dandelion, buckwheat (plant as a cover crop), hairy vetch, veronica, verbena, phlox, lemon balm and other mints in bloom, thyme in bloom, marjoram and oregano in bloom, feverfew, coreopsis, milkweeds (will attract butterflies), cinquefoil, monarda, coneflower, rosemary in bloom, stonecrop, lobelia, pennyroyal, goldenrod.
For myself, fennel is my workhorse it provides pollen and nectar for a variety of beneficial insects from lacewings, ladybugs, parasitic wasps, tachinid flies, and the occasional bee. It has a very long bloom period, but I harvest the seeds every year for the kitchen and replace it every year to keep it from spreading. Fennel is an aphid trap and invites aphids to it and the ladybug larva have a lot to eat. Fennel does have to be planted away by itself because it does not like company but protects plants up to 50 ft away. Marigolds are the second most hard working plants in my garden. They are also aphid traps so they provide food for lady bug larva and nectar for the adults and the ones I have also help with nematode control. Four o'clocks keep the rose beetles at bay and provide nectar for beneficial insects. Green onions and chives planted near other crops hide them from predators and their blooms are also visited by bees. Basil, marjoram, shiso, rosemary, chives, green onions, roselle provide nectar and pollen for foraging bees. The basil can be grown year round and the marjoram is almost always in bloom. In summer I plant sunflowers as well. The carpenter bees do most of the pollinating of squash around here and they like the long purple spikes of lavender and verbena. The bees and butterflies both like alyssum and false heather which pretty much blooms year round for me. Citrus trees bloom multiple times in the spring and summer. Nasturtiums come up every year on their own.
Controlling the ants and water controls most of the aphids on the citrus and gardenia. I don't have aphids much anywhere else.
I don't plant in rows and I try to space the plants so the tops get good air circulation and I put shorter plants between them. I cannot rotate in space since I don't have a lot of space so I rotate in time. I plant different things at different times of the year so the same space does not get the same plant year round. If they get creamed with bugs, I don't plant them for a couple of years. This is how I have been able to grow broccoli for years with very little damage since the butterflies sometimes never find it. One butterfly did find the broccoli one year but it was short lived, the geckos took care of the butterfly and the caterpillars. I picked off only a few by hand. The butterflies are coming around again. I have to move the butterfly bush that is attracting them somewhere else.
I do have insect issues. I have a lot of thrips, but I live with most of the damage because any insecticide that kills them will also kill their predators. I only spot treat for severe problems usually with alcohol. I also have plumeria, gardenia, and orchids which are thrip magnets that I don't want to get rid of, so I have to live with the consequences.
Snails and slugs are my bane. I have no predators so I am having to throw out slug bait which the birds and rats also love. The stray cat has caught a couple of rats but I think I have to do some trapping. They ate though 2 plastic containers and half a bag of slug bait. I have been clearing out the weeds with round up and that has cut the numbers of slugs and snails down, but I still have to go on snail hunts.
I do have a hibiscus which I do have to treat for erineum mites, my only other choice would be to get rid of it. It can be isolated so that is a good thing.
I have actually gone from one extreme to the other. I used to overfeed everything with miracle grow every two weeks. Now, that I do soil tests, I have cut the amount and only use low numbers preferably under 10. The orchids however, went from being overfed to hardly fed at all. The orchids actually need to be fed more.
Happy gardening in Hawaii. Gardens are where people grow.