Illegal? I wouldn't go that far (unless it actually is!! source?). Maybe against school policy but he was one of those chill teachers who don't give a fuck basically--lots of teachers break the rules and it's not a big deal. Yeah, him and Nadine had a weird relationship. He knew she was being dramatic and he was right, made her feel a lot better when he gave her money for ice cream or whatever.

Definitely unrealistic but it didn't really feel off, it was more funny than anything. They pulled it off nicely.

Well maybe not illegal, but definitely against policy at a lot of schools. Teachers have to be very careful in how they interact with students. As the audience we can see that Woody is a chill guy with good intentions, but if he was creepier and less moral he could easily be the kind of teacher that would take advantage of vulnerable students to sleep with them.

You see in the extended scene (the second time it comes around) he looks at the message she sent and helps her. They both know she is over reacting. In the end when she leaves to get the yogurt she is much calmer after talking it out.

Is it just me or it looks like she was struggling to keep a straight face during those scenes? Every time Woody responds she looks like she smiling slightly.

I'm sure his actions were against some policies. However, his performance was still very good. Also, I think the actions his character made were done intentionally. They strived to create a teacher who wasn't typical and did things by the book.