I know you have a lot on your shoulders right now, and the hardest part is not having answers.
Now there are a couple of things to think about. First of all, there may not be cancer in the salivary gland - they just have to check on that. Secondly, be sure you understand the doctor. Even if something is not OPERABLE, it doesn't mean it's not TREATABLE! Many cancers are not operable - leukemia, lymphoma, bone marrow cancer, and many other cases including some lung, brain, breast and you-name-it cancers. Those cancers are treated by chemotherapy or radiation, and sometimes both. Chemo and radiation reach cancers that are unreachable by the surgeon's scalpel or which are spread into too many areas. So it doesn't mean she's going to die! So you don't have all the answers.
If she's going to Dana Farber, that is great. It's a fantastic center, and there are satellite centers all over the area so sometimes a person can be seen at the main center and then treated with the same care and expertise at a location closer to home. People aren't sent there if they are going to die. They are sent there for evaluation and treatment.
It's great that your sister is a nurse and can talk "medical language" to the doctors. But remember that sometimes these professionals don't always put things in everyday language for the rest of us. Moreover, you sister is a nurse but she is also a daughter. She may be emotional too and not getting everything exactly straight. For example, if they are saying they have never heart of lung cancer going to the salivary gland but it "always goes to the bones and brain" - that doesn't mean your mother's cancer is going to do that or that everyone's lung cancer goes to those places. For many people, the lung cancer is TREATED and it doesn't go anywhere! That's what you can focus on. Many, many people go into remission and the treatment even cures the cancer, so it doesn't spread anywhere. If the usual route for metastazied lung cancer is to the brain & bones, that doesn't mean each individual's cancer will go anywhere. Be sure you understand what they are saying. AND, if she hasn't even been seen by the experts at Dana Farber, you're getting way ahead of yourself. You are trying to get all this info out of your mother, and she may be shielding you but she also may have too many things on her mind and may not have asked the questions you have asked.
My own mother is receiving treatment and rehab for something completely different, but I can tell you that there is no substitute for actually being at her side when the doctors and therapists come in. She misses certain things, or she asks different things that matter to her but which don't necessarily paint the whole picture.
You live in the same area as your mom, which is great. You can become involved. You are also seeing a therapist and taking some meds which you and the doctor feel are helpful for you now, so that is great. You've got to take care of yourself.
In your SWH, you say you are the baby and "such a weak person" - but you also say that your daughter needs you and YOU are the mother now, so it's time for you to step up. You also are very open about your panic issues, so try to remind yourself that it may be YOUR issues that are making this a dire situation rather than your MOTHER'S actual condition or the doctor's information. Even if one doctor said one thing, remember that there are second opinions and that doctors are often wrong the first time out. SO you need to calm down (with professional help) and you can also try to see this as an opportunity to no longer be imprisoned by weakness and by your status as the baby in the family. You are an adult and no longer the baby, and it's time to step up.
There are also tons of things you can do to use other things such as nutrition to support cancer treatments. I have a colleague who conducts a nation-wide call dedicated to dietary changes that help cancer patients. It's every Thursday and there's also one on Sundays (both evenings). A friend of mine has been using this information for about a year for her own elderly mother, who has multiple myeloma (in inoperable bone cancer) - and guess what? Her mother has sailed through the chemo treatments with a lot of energy, more than she ever had even when she was young, and her cancer numbers are improving tremendously - far better than the doctors ever expected in so short a time. And this patient is in her 80s. Yet no one has given up on her. My friend has found the call to be very informative, and her mother appreciates everything the daughter is doing to step up to the plate and help out.
So if you want to listen in, PM me and I can tell you the info and even "take you onto the call" myself so you don't even have to think. It's a listen-only call, not a participatory call, so you just need some quiet space to sit and listen. There is a huge network of cancer support out there for people just like you.
SO cancer is not a death sentence, and you will benefit by focusing on what CAN be done far more than you will by panicking yourself into paralysis.
Keep focusing on getting yourself the help you need to be able to help your mother. Then put together a series of action steps, perhaps with the help of your therapist, and let your mother know that you are not someone else she needs to take care of while she is sick but rather that you are going to be a source of strength to her.