My 10 year old has been able to shower herself, including washing her own hair, for a couple of years now and yes is going through the stage where the door has to remain shut when she is in the shower or getting dressed. She is a bit slack with keeping her room clean (we are working on it
) but is expected to put her dirty clothes in the laundry (including sorting them into the respective hampers) and folding and putting away her clean clothes. Bedtime is by 9pm, if she starts whinging about getting up in the morning then it goes earlier. She helps feed the pets and does some general cleaning, dishes, packing and unpacking the dishwasher, bringing in or hanging out the washing but these arent regular chores, just when she is asked.
After school she is expected to hang up her bag and unpack homework and lunchbox, get any notes out for me etc. She also makes her own school lunch now in the mornings. I started all three kids doing that last year as they all wanted different things and it was driving me nuts (one wanted butter on their sandwich, another didnt, one wanted their fruit cut a certain way, another wanted it differently lol, I finally told them they were old enough to do it themselves). Everything is in the cupboard or fridge and they know what they can and cant have (ie must have sandwich/salad, one piece of fruit, water bottle, some form of dairy (either cheese or yoghurt, not both) and only one snack).
With her 'parenting' her little sister, that could just be a transition thing, wanting to be in control of something when she is going through such a change of circumstances that she feels like she has no control. Go gently, but just explain that you need to make certain decisions for her sister. I know even now my DS tries to 'parent' DD1 (she has Aspergers so he gets stressed when she acts out, especially at school or in social situations) and it causes all sorts of clashes between the two of them. I need to sit my DS down when he starts up and just calmly explain that if there is an issue he needs to come to us and we will decide whether it is something that needs correcting.