Why exactly would Arthur be a psychopath for "pretending" to be their child? Yes, he's a middle aged man but he got thrown into a child's body with no knowledge of world he was in. He couldn't talk at first either and even when he could, he couldn't exactly say "hey, I'm not actually your son but a 30+ year old man". Remember that he used to be very cautious and cold as that was how he had to survive in his original world. He didn't know what his parents' exact reaction would be and they could very easily overpower him as he was a child at the time. Not to mention that he did have an attachment to them at the beginning since this was the family that he'd wanted in his previous life. Of course, it was somewhat superficial at the start but as he spent more time with them, he developed a genuine love for them.

Judging from his parents reaction (not saying that their reaction was not justified), he was correct in making the choice to not tell them until he could properly defend himself and could also give them time to digest that information in the time that he would be away. By defend I mean, if they come to the decision that they don't want to associate with him anymore, he has a place to go. 

I sorta agree with the pedo part thought, since Tessa is still a minor.

However, the pedo part is iffy depending on how you look at the situation, it's like if an 1000 year old g** that looked 20 was in a relationship with a 20 y.o. Since Arthur is technically the same age, it's just that his mental age is much, much older. Regardless, Tessa isn't of age, so yea.