Are civilians allowed to send objects into orbit, or even leave orbit, like send something to the moon or deep-space? If they can what kind of paperwork/waivers/licenses etc. need to be obtained before they can do it.
Sure, private companies do it all the time, and there's nothing (other than money) stopping you from doing it too. The licensing requirements vary depending on the country or countries you want to operate from. In the United States, the FAA issues licenses for launch and reentry. NOAA issues licenses for remote sensing, and the FCC handles radio communications. If you want to control the whole thing - from launch to operations of the craft - you'll need whichever of those are applicable.