Eric is an alienWe are shown that The Last Starfighter game exists in this movie, so both movies are set in the same continuity, where aliens can and do come to Earth. Eric was a little kid when he came to Earth: this means his parents had to flee from their home planet and took him with them to protect him. The reason why they fled is that their planet was conquered by the Ko-Dan armada, by which Eric and his parents could have been killed. They chose Earth because Earth is not a member of the Star League, so the Ko-Dan armada would ignore it unless a potential danger for them was present there. Nothing unusual was found in Eric's house, which means Eric and his parents did not come to Earth in a spaceship: they could fly just like Eric does, and they could even fly through space without the need of a spacecraft. They only took a plane to pass as humans, which unfortunately, led to their death.
Eric is telepathic, not autisticIt is explicitly stated that Eric felt his parents dying. This means his people are telepaths, so they don't need to talk to communicate, nor they need to express themselves with body language, and they lack an instinct to do so. Eric was too young to learn intellectually how to communicate like a human, and the only people who could teach him died, so he never did. His telepathy only works with other telepaths. When his parents died, all of his possible contacts were "shut off", so he found himself completely isolated.
At the end, Eric flew to another planetIt would have been very dangerous for him to show up anywhere else on Earth, so he went off into space. He probably knew about the war on his home planet, the Star League and Rylos by sharing his thoughts with his parents, so maybe he went to Rylos to be safe.
Eric was a mutant, he just never heard of Xavier's school.