I think he is moving too fast

Hey guys, i’m 26F and i’m currently going out with 27M. I’ve been single for a long time and honestly i’m ready for a relationship BUT i do like to take things slow and get to know each other for a month or so until i’m sure i want to date him. We’ve only known each other for a week.
On our first date, we went out for lunch then he brought me to meet his friends… i felt a little uncomfortable at first and i told him exactly that. But he said it’s because he likes me and is sure about me that’s why he is quick to introduce me to his close friends.
Then on our 3rd meetup he introduced me to his mom (not formally), basically we visited his house and his mom was there. He also insisted we start using nicknames (baby, babe, etc), i told him no because i don’t want to get in too deep… at least not yet.
He said it’s normal for him to introduce me to his friends and family if he is sure about someone.
We hold hands and hug which are fine to me but still i’m confused because i’ve never done any of this things with a guy in a week.
I told him some of this makes me uncomfortable because i feel like we’re moving too fast. He wants to do things like we are dating but he never really properly took me out on a date except for that one time. I told him more than on one occasion that i want to do things slowly. But he will get mad if i don’t use nicknames on him or refuse to touch him – i don’t know if this is a red flag.
What should i do? I like him but not to the point where i want to be in a relationship with him. Plus, we’ve only known each other for a week and i still want to get to know him first.