Please find all you need to know on Wikipedia.
Does Orgone energy exist?
No. Mr. Reich even had one of his experiments checked out by Dr. Einstein. Result? Busted
Reich supplied Einstein with a small accumulator during their second meeting, and Einstein performed the experiment in his basement, which involved taking the temperature atop, inside, and near the device. He also stripped the device down to its Faraday cage to compare temperatures.
In his attempt to replicate Reich's findings, Einstein observed a rise in temperature, which Reich argued was caused by the orgone energy that had accumulated inside the Faraday cage. However, one of Einstein's assistants pointed out that the temperature was lower on the floor than on the ceiling.
Following that remark, Einstein modified the experiment and, as a result, concluded that the effect was simply due to the temperature gradient inside the room. He wrote back to Reich, describing his experiments and expressing the hope that Reich would develop a more skeptical approach.
Did the US government burn his books and jailed him?
Yes. It's a undisputed historical fact. The burning came out of an FDA order that orgone accumulators were an illegal medical device. They ruled that any publications that explained how to make one or use one, or the use of the mythical "orgone energy" in healing disease, had to be withheld or amended, and any existing copies were to be destroyed in a fire. The order explicitly says Reich could re-issue the books with the offending passages removed.