Ladybug Beetle

I'm not an expert (at anything really) so this is the only part of your question I can answer:


yes, definitely. So if you find one in your house, you should never kill it. Take it outside and say, 'Ladybug, ladybug, fly away home....' and you will have really good luck (at least for the rest of that day- my grandmother taught me that).

However, if you live in southern Wisconsin and you have swarms of those ladybug imposter Japanese beetles who breed in the soybeans and appear in huge numbers after every harvest, kill the shit out of 'em. They're hell on the trees.

true ladybugs are very beneficial to gardens, they feed on aphids

The number and distribution of spots helps to identify the species of ladybug. These are in a large family of beetles called coccinellids (Coccinellidae), and there are MANY coccinellid species in North America. Many species are marked with spots or bands. With few exceptions, both larvae and adults are beneficial as predators on aphids and other pests, often resulting in effective control of these plant pests. A few species are phytophagous and are crop pests.
I can't speak to how lucky they are, but the deliberate introduction of a non-native Asian ladybug has driven at least a couple of our native Ladybug (e.g., two-spotted ladybug) numbers down dramatically. Nobody has really noticed, because we just think of a ladybug as a ladybug.