This question I actually know about because it used to kick my butt in interviews. They aren't looking for you to bare your soul about how you feel about yourself.
They are mostly looking for a window into how you evaluate things and solve problems. So by listing your strengths, you are showing what qualities you have that would make you good at the job or help you fit in within that environment. Remember, the interview isn't just about finding out what skills you have because you already listed them on the resume/cv. It's about getting a feel for your personality and whether or not you would fit in.
It's also about you getting to know who you would be working with and finding out if you have good chemistry. Remember, you are interviewing them as much as they are interviewing you. When it isn't all about you, it's much easier to relax and be yourself.
The question about your faults isn't a chance for you to tell them how much you suck. It's a chance to show off your problem solving abilities. I never mention a weakness without mentioning a corresponding trait that balances it or talking about how I work around it so that it doesn't get in the way of things I want.
One of my "weaknesses" in the work place is that I tend to be a perfectionist, which can slow things down if I get stuck on something, so I balance that by being excellent at prioritizing and managing my workflow so that I can see when it's time to let something slightly imperfect get past me so that things don't get held up by something that probably isn't broken the way I think it is. If it is, I can fix it after it's been proofread by a few people.
In the last company I worked for everything went past at least three sets of eyes, most often six sets. Generally, most printed things will go past at least one proofreader and one editor. No matter how many eyes see a thing, a glaring mistake can still be missed because people are fallible.
Dealing with death and loss isn't easy for anybody. You don't have to sacrifice your sense of compassion to get through it. You don't have to become cold and hard inside.
However, you do have to find a way to cope with it that works for you. I would suggest finding people you respect, people who seem to respect others and display compassion for others, and ask them how they deal with loss or how they suggest others deal with it. It's important to ask people you respect for their compassion because they are the ones most likely to give you an answer that helps you rather than giving you an answer that needless discourages you (because some people do believe that cynicism is the best remedy for loss and that won't be a helpful answer for you.)
I work as a caregiver, so I've had to take classes on coping with loss. The thing that always comes up is take care of yourself first. Do your best to get enough sleep, food, water, and exercise. Do your best to make sure that you have fun and do things that affirm your life. Pay attention to your needs and meet your needs as best you can. That keeps your energy levels up so that you can be successful at helping other people meet their needs. It keeps your energy levels so that you can more easily deal with loss.
Dealing with loss never gets easy, but if you are affirming your own life, it can be something you can cope with. Build connections with your friends and family and surround yourself with a strong emotional support network. I don't just mean people who will be directly supportive, but people simply doing things with you and being close to you is life affirming and emotionally supportive.
It isn't self-centered. It's self-filling. You're like a cup. When your needs are met, you're full emotionally. That means you can pour out compassion and support without draining yourself dry and doing damage to yourself. When you're only half-full or nearly empty, you are deeply limited in how much you can pour out before you're drained dry and have nothing to give. When you have nothing to give, you feel tired and wrung out and tend to be more calloused and less compassionate. You can hurt people without realizing it. So, you want to keep your cup full.
The important part of dealing with loss is finding a way to accept it as a natural part of life. Some people turn to religion for that. If you can believe that spirits move on to something better, you may be able to feel like you helped them along their journey even though you couldn't lengthen the time of their journey here. Some people don't need to religion to feel that way because what we do in this life is important enough without the sense of external reward. Even if you lose a patient, you did a good thing by helping them during their last days.
In fact, this is where compassion is the most important trait for a doctor. You can't make everybody healthy, but you CAN help everybody be as healthy as possible for them and when you can do that with compassion, you not only help heal their bodies, but you can help heal emotional wounds.
I've been abused emotionally and physically by doctors who assumed that my weight meant I didn't deserve their care because I was obviously killing myself by degrees. They thought my food and exercise logs were lies and yelled at me and treated my body roughly. A doctor who can be compassionate is the most important thing in the world to me. It took a decade to find one and I'm so relieved everytime I'm in his office because he shows genuine respect for me and listens to me and helps me instead of yelling at me for not doing enough to help myself.
He's a cardiologist in a town full of elderly people. He loses a lot of patients. I think he keeps his cup full in a lot of ways because I've never seen him look tired or calloused.
Please do whatever you can to get through med school, if you are able. The world is desperately in need of compassionate doctors.