First of all, congrats to you for doing such a good job raising her, and to your DD for finishing school, getting a job, etc.
I lived at home until I was 30, but only paid rent for part of the time. When I first graduated from college, and living back at home, my parents didn't charge me rent, initially. but in my case, I commuted into NYC, for an entry-level job, which paid not a whole lot. So anything I could have paid them in rent, went to my monthly bus pass. that being said, I had certain chores I was expected to do, and I was also responsible for any phone calls on the bill (didn't make sense for me to get my own phone line as I didn't make that many, and this was way before bundled plans, so you paid for LD separately) I also paid for my own groceries, i.e. stuff for lunches, and would chip in for other things.
I do know that fall, my car insurance was due. My mom said sign this (the title), give me $5, the car is now yours, so you are now responsible for the insurance, gas, and maintenance. I had the car at school my sr. year, and my parents paid for about $10 in gas a month (back in the late 80's when it was under a dollar a gallon) and would pay for it when I drove back and forth. Anything else, was on me.
After I left that job, and was working locally, I want to say they charged me about $200 a month. I still had chores, etc. and nothing else changed. I paid rent until I could afford to move out on my own, aside from a short time when I had gone back to school, and hours at my temp job were cut to PT. they "suspended" the rent for that time.
Sorry that was so long winded, but my advice would be to figure out what she might pay living on her own, or with roommates, and charge a portion of that. I can't say a specific amount not knowing where you live, and what rents might be. And also set some ground rules. Chores you seem to have covered. But I know for me, my parents dind't mind if i wasn't home for dinner, as long as I let them know.
As for the other stuff, even though she's working, it may take time to save up, and if she has loans from school, etc. she may not have that much disposable income. I'd say for anything else, play it by ear initially, see how things go, and go from there. I know my parents did hlep me out several times with some car repairs, since i simply didn't have the $$, but i always paid them back. no matter how long it took.