Kph,
Welcome to BPD Family. Sorry you are here, but you are here to support your dear daughter, and that is very commendable. This is a judgement free zone, and most of us can sympathize and empathize with you. Being mindful that each case is different, what works for one person may not work for another on specifics; however, general themes are helpful for managing the situation.
With the diagnosis you now know where these destructive behaviors come from. More often than not a diagnosis comes from an in-patient facility after an 'attempt' or a psychiatric evaluation - if this is the case use the psychiatrist to organize what the next steps are.
There is full hospitalization that can last days to months, sometimes followed by php (partial hospitalization protocol), and more often than not iop (intensive outpatient therapy). The more support that you and her family can give her, the better.
I see you have asked many fabulous questions, each of these are clear and concise - the answers are not.
I will put your questions into italics, and respond briefly on each one.
I feel like I’m drowning. I think each and everyone of us has felt that way. I was completely overwhelmed about 10 days after I was informed of this when the magnitude of this really hit me. Find support groups, including BPD Family. Use the hospital's resources for guidance, they generally have a good set of directions you can start with, and where to go. If they offer classes, take them. The more educated you are on this, the better. There is also a lot of information on this site, explore the tools section.
How do I help her without hurting her? It is next to impossible to help her without hurting her emotionally. The best you can do is to validate her feelings, and not validate the invalid (facts she 'makes up' to match her feelings). If she lashes out at you (and appears hurt), it is because she loves you - this is the paradox of mental illness. Her feelings are genuine, but are magnified by many orders of magnitude than a normal person would experience.
How do I give her clear boundaries 
and expectations? Setting boundaries, refer to her psychiatrist/team on which ones to set initially, and then expand slowly on which ones to set next. These are boundaries that you set for yourself, and what you can enforce, as borderlines do not respect boundaries. I am 18 months in, and I am still figuring this part out... However, once you establish a boundary, you must be willing to enforce it with the consequence of not following it consistantly - if you don't do it one time, it will take weeks and be much more difficult to re-establish the boundary.
Your daughter is the same age as mine. Best place to set expectations is to duplicate the ones that her school sets for her. Respect authority (you or a teacher), expected to do work on time (chores or homework), etc.
How do I support her through setting goals?She must set her own goals. However, you can make suggestions; however, be prepared for her to reject those suggestions. You can steer her goals by setting boundaries that would encourage good behaviors.
How do I help her survive?1. Self-care (seems counterintuitive and selfish), you need to make sure you have the energy and stamina to help, make sure you fill your cup, so you can share that with your daughter.
2. Learn about BPD. You wrote "
I’ve done so much reading in the last 12 hours.". I don't mean to scare you, but you have only begun learning about it. This is a process and the timing is different for everyone. Make sure you do self-care, and don't exhaust yourself doing research.
3. Learn about communication techniques, the easiest one to learn is using "I" words. There are a lot more. Borderlines need an excessive amount of validation for their feelings. Be genuine, and do not validate the invalid, redirect, and focus on what you can validate. Give reassuring words like "You got this", "We are here for you", etc. And once she has progressed a ways and is regressing you can change that to "As long as you are working with your therapy team, we are hear for you".
4. There will be setbacks, all the way to ground zero, this is rough. It is like learning to ride a horse, and it throws you, dust off, heal, and try again, over and over.
Statistics are scary. She’s had 7 attempts. How can I help prevent those? Yes, they are very scary. My pwBPD has had 6 attempts. Best way to prevent them is with a 'nuclear deterrent level boundary' - specifically you will dial 911, and have emergency services deal with her, and get her back in the hospital. It can go from a threat, to a life-threatening emergency in seconds.
Best way to prevent them in the future is to have a therapist work with her on this. Encourage her to call/text 988 when she feels like she is suicidal, that is what it is there for 24/7.
There are four levels of suicide ideation - 1. Having the thought (ideation), 2. Having a plan, 3. Having a means to the plan (gun, pills, knife, etc.), 4. A timeframe - for BPD's due to the impulsivity, you can go from 1 to 4 in under a second.
How can I learn what’s impulsivity speaking versus a factual thing she’s considering? I am not sure I understand this question, could you reword it for me?
Where do you begin? With your daughter's treatment team. Followed closely with self-care. Here at BPD Family and anywhere you can find help.
Take care with self-care.
