Congratulations on your new home.
First of all roses are pretty hardy once they are established.
They bloom in cycles. So after they bloom cut the roses back above a node that has five leaves. I cut out all the spindly growth and only cut back on branchese that are the thickest. Always cut above an outward facing node to the new branch does not grow into the rose. Cut out the rubbing and crossing branches too either back to the main branch or to an outward facing node. Make sure you have a clean sharp pruner. Put a sprayer on an alcohol bottle and spray the blade between cuts to disinfect it. The pruners should be washed cleaned and oiled after each use. Between roses get a small torch and heat the blade a few seconds. This is to prevent transmitting diseases between the roses.
Feed the roses. If you do not have children and pets Rose Care 3 in 1 will feed and protect against diseases and pests for about 6 weeks which is just about when the roses should come into bloom again. Add a couple of inches of compost to the ground around the rose but not up agains the rose stem. Keep compost and mulch at least 4 inches away from any plant stem or tree trunk. The compost will help hold down weeds for a short time and help to hold moisture as well.
Roses are difficult to grow organically, you can use organic fertilizer but roses are heavy feeders and like a slightly acidic soil. There are many different rose and flower foods on the market to choose from. Do not get fertilizer stakes. They are expensive for what they provide. If you do not use rose care you will have to fungicide whenever it rains and the humidity is high. Bugs need to be identified. Aphids, mealy bugs, and crawler scale can be sprayed with insecticidal soap or horticultural oil, but you will have to repeat treatments every three days until they are gone and you will need to spray again if they return. Scale, rose beetles are harder to kill. I actually use a brush and soapy water to scrub off the scale from my roses.
Rose beetles are another story. Short of using systemic insecticides you just have to do the best you can.
I do not have Japanese rose beetles. I do have Chinese rose beetles, unlike the Japanese rose beetle, Chinese rose beetles feed between dusk and 10 p.m. so I control them with light. I plant my roses under a street light and guess what, I only have holes in the roses that are not under the light. I don't have too many of those either since I have a lot of geckos, anoles, and skinks in my yard and they like to eat beetles. Hopefully the birds that are hanging around eat more than my lettuce, tomatoes and strawberries. I plant four o' clocks in the yard. I found out by accident that they trap and kill beetles that try to eat it.
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Happy gardening in Hawaii. Gardens are where people grow.