Yes, it is possible. Yes, Honda engines used to turn the opposite of most engines, until around 2002 model year, since, they turn the same. The CRX was a very popular shell to accept newer engines and all you need to know can be found on the many Honda engine swap sites. There are kits and harnesses the will help with most any other Honda or Acura engine you can get.
Pick the engine you want based on you project and start from there. Be sure to get every part from the engine, transmission, harness, ECU and sensors. The mounts can be tricky but Most any Honda shell/engine combo has been done so kits for most are available.
An example is someone on here put the Insight drivetrain in a CRX.
Good luck.
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