How to deal with a very weak student?
Some short-ish advice:
First: Realize that you can't save everyone. I'm on the other end of this, teaching at the community college, which is something like an academic M.A.S.H. unit. Some people you have to realize are, most unfortunately, unsaveable ("black-flagged" in medic parlance). The weakest students are, oddly, the ones most resistant to suggestions about switching to easier courses (I tried this twice this semester to no avail: see Dunning-Kruger effect).
Second: Set boundaries. It's probably an abuse of your office hours that this one student is taking up all of them. Proper usage is, as you say, 10-15 min for a particular question or issue. For a particularly weak student like this I may say, "Let's say we have 30 minutes for this." Require that she ask about a particular homework exercise that she can show prior work for. Do not just regurgitate the lecture wholesale.
Third: One student failing should not cause administrative hell. Students will fail and this is a normal part of the institution's function. If she does complain then (at least where I am) the instructor is given the benefit of the doubt. The majority of the time, a student in this situation has a record of failing other STEM courses. (If it does cause hell, then you have my enormous condolences for a degenerate administrative system.)
Fourth: It doesn't hurt to document what you efficiently can. I keep a digital gradebook via the learning management system; occasionally a student complains, my department ask for documentation, I turn that over (showing multiple documented failures), and that's the last I hear of it. After grading, I actually run all my tests through a bulk digital scanner so I keep a copy before I hand them back (in fact: I make all my tests on one sheet of paper to assist this; takes about 1 minute at the school's feed scanner). This actually hasn't been seen by anyone else in the few years I've been doing it, but it's there if I do need it. Also it's good for me to reference as documentation and examples in the future.
I haven't seen this point mentioned yet:
She is a transfer student from a community college, and no one else has any data on her as this is her first semester
When she does not understand a concept, she bring her notes and says that the class was unclear and that I should explain it again to her
her idea of academic improvement is to consistently show up to my office hour and listen to me talk
She is doing things that work well in secondary school (a.k.a. high school) - she's working hard on her homework and making maximum use of your office hour, and so on. She probably thinks she's working hard and doing well. In school, the exam questions tend to test whether you've learned exactly what was told, not more.
But at some point a student has to learn that university isn't secondary school. It's much more about working on your own than about absorbing from a teacher. Not everybody knows that when they start. She doesn't realize she needs to change her way of studying.
So I think you could also have a conversation on that, she's there in your office anyway.
Not a full fledged answer, but some tips:
Prepare appropriate responses to complaints. Do not defend yourself, but state your expectations. For example, for "This question is not doable." do not answer "But is doable like this..." but respond "Being able to do questions like this is part of the expectation for the course." For "I did not understand the class and I have no idea where to start." answer "Students in this class are expected to work through the material and be able to grasp the course material. The office hours are for additional questions and occasional clarification."
You may take some time to review her performance with her based on facts. Something like "Let's see if your difficulties with the questions are reflected in your other performance. On previous homework you did like... while in the quizzes the picture is very different. Note that the final grade will be determined like... and that your current performance may not be enough. To be able to pass this course you need better performance in... " For the last point it is important to not judge the person but her performance.
As for "I have no idea where to start." Use the Polya questions "What is the given data?" and "What would the answer be?" Do not answer these questions under any circumstances but stress that every student has to be able to answer these questions on his own. You may help a bit and reiterate the question several times (from my experience, most weak students need to hear the question more than two times before they even start to think about the answer) but you shall not provide the answers even if office time is over and not even if it is the second or third time the student comes to office hours with this question.
Ignore the remarks like "The lecture was unclear." and respond "What question do you have about the class." Focus solely on the student’s learning. Sometimes I would go as far and say "If you don't have questions about the class then I can't give answers."
Do not suggest an easier class but try to make it her idea. For example you could drop the line "The expectations for this course is... but that course has the expectations..." Be sure to not imply that she will make that other course for sure.