I know that my parents started making me do dishes around age 8 or 9, and I guess I hadn't really considered if that was normal or not until now. Is it normal?
It's normal. My parents didn't have a dishwasher until I moved out, so I was made to do it or help. Before remotes I also had to get up and turn the channel for my dad. All these time saving devices really help kids the most ;)
I don't know if it's normal, but I was washing dishes at a similar age and later cooking for the family as a teenager.
My children are 3 and 5 which is why they're not much help with washing/drying and why the bedtime routine is more involved - bath, drying, brushing teeth, packing up, reading, answering questions about why they have to go to bed, why it's still light outside, how they are actually tired and so on.