Your daughter is struggling because she hasn't learned good study skills. It takes time to learn them, and it's difficult without someone helping you along the way. That's where you come in. You have to teach her. Help her find a good, quiet place to do her homework, and make homework time part of your daily routine.
Your psychologist friend is right. Punishing her isn't going to work, partly because she doesn't even know what it is that she is doing wrong or what she should be doing. So teach her.
"My daughter forgets things she needs, doesn’t study, I find out about tests after the fact, doesn’t write down assignments ... "
This is totally normal behavior for 6th grade (just reassuring you that lots of 6th graders are still learning). One of the best things you can do here is ask her about this every night. "What did you do in English today? Anything due tomorrow? Any tests/quizzes coming up? Any papers/projects? What did you do in Math today? Anything due tomorrow? Any tests/quizzes coming up?" Do that for every class she's in. Make asking those questions part of your daily routine. She'll begin to do that for herself.
Keep in mind that you should already know the answers to all those questions. Your school's website should include an area where all the teachers post their lesson plans. Our teachers update them each weekend so that by Monday morning we can know what is going on that week - what they are doing in class each day, homework, tests, projects, presentations, etc.
If you aren't sure where the lesson plans are, just email one of the teachers and ask. I'm sure they will point you in the right direction. If your school doesn't do this (they really should, and you should suggest that they begin to offer this for parents) ask each teacher to give you a list of what's coming up so that you can help your daughter.
These are learned skills. She isn't going to master them right away. That's ok, thought, because she's only in 6th grade. Middle School grades are just for practice. This is the time for her to learn from her struggles and experience so that by the time she begins high school she has master some or all of those skills.
This is the time for her to learn those study skills. Just keep helping her learn.