Splitting the bill with my bf/his son. And Hypocritical play time?

So my boyfriend (of 8 months), his son and myself went to get food.

The bill came up and he's tight on money, so I offered to split it. But when he handed the waitress the cards he told her to put himself and his son on his card and I just pay for my own. That's not what I meant by splitting it.

I don't mind taking turns paying. but any time we go out to eat with his son he doesn't let me help pay for anything the kid eats. We've already talked about it I don't remember the verdict, this is the second time it's happened. it kind of sucks because I don't mind helping? Just makes me feel excluded. Am I over stepping?

....

He's also been kind of uptight with how I play with his son this past weekend too. But he plays with him the same way so it's kind of hypocritical. I know people are particular with their kids so I'm not even upset by it, but I kinda don't understand when were talking about getting our own place? What happens then? Am I just not going to ever watch his son? That's not realistic. (We have a roommate rn)

I've helped raise my siblings and he knows that. He's never seen me interact with other kids before so he doesn't know how I am with kids.

it's hard for me to figure out the boundaries because it's like one things okay one weekend then the next weekend it's not. And I know he has all the right to set those boundaries, it's just confusing because they constantly change person to person/day to day.