Good translation so far. Not the best, but I have seen much worse.
And I don't like how he keeps lying to the girls. I mean, they already pretty much figured out that he is from another world by seeing how he knows absolutely nothing about their world. As long as he doesn't tell them about the ring and only says "I have the power to travel between worlds" there should be no problem. Even if they didn't believe him, he could just prove it by disappearing right in front of them.