Electromagnetic spectrum. Red is less energetic, blue is more. Light gets redshifted when it has to move a farther distance due to the expansion of space.
I'll be honest, I only know of them detecting them due to the transit of the planet in front of the star. I guess since they are technically black bodies we may be able to detect them by their own light, but idk.
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Most planets discovered are large. A large planet will cause its star to wobble a bit as it goes around it. Correct on the rest.