It's very difficult.
First off, a friendship does have to be two way. If it's not, you're a carer ... and that is not a position you are in. So you need to get something out of this relationship as well as give something.
The sister is probably partially a carer in practice and when you are very deeply concerned for someone who is desperately needly, sometimes you can start to think that everyone else should help too. But your relationship with her is different and you do not have responsibility for her. It is a friendship.
One of the whole things about borderline personality disorder is that people around need to keep very firm borders. Her sister is highly unlikely to be trained in it and may have been sucked in a bit. She might also feel desperate and be lashing out But again, the lady with BPD is not your responsibility. Someone with BPD may have a lot to give but can be tricky and yes, sometimes people reach the end of their tether.
The snapping probably is part of the illness. Also at a guess, so is the boastfulness. If you have that low self-esteem you can cling desperately to the things you are proud of because it gives you some validity. Something to be proud of that others might respect .. because it's hard for someone with BPD to feel real self respect.
Whether she is being an arse or whether it's the condition, I think myself that if you wish to keep in touch the best thign to do is, when she starts snapping, to quietly make your excuses and leave. BPD is an illness characterised by lack of emotional maturity and in some ways, (kindly) treating them like a slightly immature person, a 10 year old or 15 year old, can help. Boundaries! If you leave whenever she snaps, then eventually she will hopefully manage not to snap. About the , questioning you over something you said, if you can the best way I know to deal with it is to answer once or twice or three times, then to smile and say that you have explained it, that you find it difficult to be asked over and over and could you both please talk about something else.
Also, from what I'm aware of there is a genetic componant to BPD but without doubt what actually triggers it is extreme, appalling and often repeated stress in childhood. Unfortunately, and I know this for a fact, those triggers may actually not be something that they consciously are aware of.
It sounds like this lady is really trying hard to engage in treatment. It does sound like you do like her. It might be nice if you can retain some sort of friendship, even if you have to take a step back - if you able to enjoy her company sometimes.