All of those things are completely reasonable.
My daughter is 6. October birthday.
Showers, just this week she started taking a shower all by herself without us helping (turning on the water, etc). Although you may still need to help with all that hair. Maybe help her soap it up after she tries first, but then she does the rest of the body and the rinse off.
Toothbrush. Again, my daughter can do these things, but if she tries to convince us that she is TOO tired to do it and can't we just do it for her. Just last night I left her to brush her teeth while I took a shower. She came in and said that she had brushed her teeth AND flossed. I was impressed and skeptical at the same time.
Snaps and buttons. Yes, she should be working on this. Along with tying her shoes.
Dirty clothes. Yes she should be doing this. My daughter calls her hamper Bob. When she picks up her clothes she says, 'time to feed Bob!'.
Lunchbox. Yep, unpacking the bookbag and lunchbox next to the sink is completely reasonable. I mean if she can carry it from the classroom to the lunchroom and back, carrying it from the bookbag to the sink at home is far easier.
Meal time. Cleaning up is what we are working on too. If she is truely done, then all plates, bowls, utensils are taken to the sink. The napkin in the trash. If she doesn't want to do that, it means to us that she isn't sure she is done and she has to sit back down and eat some more. If she is done with her meal, but not her drink, she is allowed to put it in the refrigerator for later. You should have seen us when she decided to buy lunch at school the first time. We had her practice carrying a fake tray and food from the stove to the table and then to the sink for cleanup since that is what she would have to do. It was pretty funny, but now she loves buying lunch. That has helped alot in the cleanup after dinner since that is what they do at lunch.
Another item we are working on is laundry. Both my kids now have to bring their hampers to my room and help me sort the clothes in to piles by color. If the hamper is too heavy, I will help them carry it, but they have to sort it. They then help me take the clothes down the hall, slide them down the stairs (a catching game where they slide the baskets down to me) and then to the washroom.
Clean their room. At least once a week, they both have to straighten up their room so we can vacuum.