She has the perfect chance to sneak a little extra in the morning and won't take it up because she can't be bothered to learn the controls.
No, she shouldn't be 'sneaking' in tv watching. Either give her permission to watch it in the morning or not.
The best thing would be to say when you wake up you are not to wake me. I will come to you when it is time to get up. You can either stay in bed and read quietly to yourself or (quiet activity of your choosing) until I come for you.
Two choices is enough. You could even get her to decide the night before and get the activity ready to remind herself when she wakes up.
Also, tell her that if she breaks the rule there will be a consequence - this could be 'time out' or loss of some privilege.
If she follows the rule she could earn stickers for a chart and build up to a special treat for being so thoughtful of others and taking responsibility for herself.
I would definitely advise against this - Ask her how you can improve your sleep, tell her you sleep badly because you worry about her...
You sleep issues are not her problem and she should not be made to feel responsible for that.
Or this - ...some cereal for you which you will wolf down even if you hate it obviously.
It's time for some honesty. Say what you mean and mean what you say. You don't have to pretend to like food to get her to behave well. That would be more suitable for a 4 year old in a 'yum, yum, delicious cereal, you have some, sort of way'.
She is not being bad she is being a 7 year old child who wakes and wants to be with her mother.
She is old enough to know that she cannot disturb you during the night unless she is unwell or genuinely in need of comfort. Just wanting to play is not a good enough reason.