Answer: Definitely remove any flower stems as soon as you recognize them. If you don't pinch them off, your plant will go to seed and die out. Frequent pinching will keep your basil plants bushy and attractive. Simply pinch the stems back to a set of leaves (anywhere on the stem). New stems will develop wherever you pinch them back.
Japanese beetles are a pest both in the larval (grub) form and adult form. It sounds like you are having trouble with the adult beetle eating plant foliage. Here's a variety of options: Protect plants with floating row covers in late spring/early summer as adults emerge. (Be sure to check under covers anyway.) Beetles are sluggish on cool overcast mornings or evenings. Shake them off plants onto sheets of paper to squash them or into containers of soapy water. You can also handpick them. There are Japanese beetle traps that have a sex attractant to lure males and a floral lure to attract females and males. These are not a cure for a big infestation however. Attract birds and insect predators which love to feast on the beetles. Plant pollen and nectar plants to attract parasitic wasps and tachinid flies. (Note that if you spray chemicals you are also killing the beneficial insects that help keep others in check.) There are some sprays based on Neem that may be successful.
Best wishes with your garden!
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