Saiki doesn't get sick. To seem like a normal person once or twice a year he'll pretend to be sick, heating his face up, using an illusion to sound sicker, and wear a mask.

Eventually Saiki warms up to the fact that they have cats. Does he pet them? No, but atleast he doesn't hate them as much as he used to.

Saiki never did end up saying "oh wow"

Saiki thinks of Yuuta as a little brother sometimes. He uses him as an excuse to avoid socializing and meeting up with people, and Yuuta gets a free babysitter. Saiki doesn't just do it because he's asked to or owes the kid for helping him, but he eventually cares for him like a brother, and sometimes wishes Yuuta was his brother instead of Kūsuke.

You know how in the show Saiki never opens his mouth to talk besides two times? Well I feel like while he thinks responses to people he usually doesn't make them hear the responses. The people he is friends with just go off of his facial expressions to guess his responses, unless he's talking to them spastically and gets a response from them, then he actually had them hear what we thought.
He just attracts people and has friends even though he doesn't really talk, make an effort to hang out with anyone, and, earlier on in the show, doesn't even want to be near them.