When I was ten, I experienced my first existential crisis. It was motivated by severe doubts in the faith I was raised in and its potential implications for me in an afterlife. It was difficult to let go of the terror of hell, especially when it was fuelled by OCD. I appreciated fully for the first time the tininess of the human lifespan in comparison to endlessness. At the time my OCD was also powering an intense fear of contamination and infectious disease, and I was suicidally depressed (my wishes to die being more about a fantasy of escape from suffering and the burden of existence rather than actually actively wanting to die meant that a belief in hell for unbelievers precluded the possibility of me ever truly feeling happiness again), so it frightened me even more to think that hell could be worse than what I was experiencing while alive.
It took two things for me to deal with this fear: acceptance of my crisis in belief and acceptance of my mortality. The inevitability of a someday death impressed upon me a calmness, because I stopped actively resisting it in my mind and turned my consciousness to other things. I think, especially influenced by growing up as sick, I didn't need to renounce a feeling of immortality, nor did I need to deal with the idea that there would be a world without me (a fear of not leaving a legacy, for example)...
Another thing that helped was history. Perceiving the immenseness of even recorded time, of how many people have lived and died in that time, and imagining their progressions through their life, including many influential people who died suddenly or young (because there tends to be more information about influential people and vice versa), made me feel less alone in the face of death. It made it feel like a conclusion rather than a termination.
When I was seriously ill when I was seventeen, I made peace with a number of things that had happened when I was alive and began to learn to let go of certain people and pain. It meant that I could begin what has been and will continue to be a long healing process. And the fewer regrets I had, the calmer I was about going into that operating theatre. Likewise, the more directly appreciative I was of the value of my own life and the world around me, the more grateful I could be to ever have lived, and consequently less frustrated to be powerless.
Since then I've learned I'll be sick that way all my life and die young because of it. I expected that to be harder... no, it's mostly just isolating. What I fear is that I'll die alone, or that I'll never accomplish anything I want to when alive... but it's that fear that gives me the drive to do the things that matter to me and live in what I believe to be the right way; these are things that are more important to me than not dying, which is unavoidable and carries less value with it.
To be honest, not fearing death is a matter of (in my case, probably a strange) perspective and/or emotional control. If I ever find myself dying, perhaps I'll be afraid... I wouldn't be surprised, it's an entirely ordinary and sensible reaction. But there is nothing I can control about the fact my death will happen eventually, and so I simply learned to stop fighting it and move my emotional energy to things, like myzozoa said, that I can control myself and that are worth caring about. It's the same with coping with my genetic disease... I can't control it, so I don't fear it, I just try to do my best to respond to the situation as it happens.
With regard to Question 2, one thing that actually sort of horrifies me a bit is leaving aspects of myself behind, but that's a personal squeamishness.
