To answer your first question, i learnt to manage anxiety and depression and live in the moment using mindfulness meditation (which also has it's origins in Buddhism). It is really a way of bringing awareness to everything we experience. It can't make every moment a good one but it can make the bad ones easier to bear.
Instead of being overwhelmed by the sensations we experience in response to events, those sensations are broken down to thoughts, feelings and physical sensations. When we do this we can stop the chain reaction that leads from rumination to physical anxiety. It is one of those things that is very simple in principle but takes quite a lot of discipline to apply. I can link to some resources if you think it is something you may be interested in.
I can't really answer the second one since i have a different view, but will have a go! Someone earlier mentioned the ego being the main problem in accepting the finality of death, the fear that our individuality counts for nothing in the big scheme of things. This is absolutely true, but i think, for me at least, as an individual i have no fear about ceasing to exist. What i fear is separation, especially from my child. Having a spiritual belief obviously relieves that to an extent, but i am acutely aware that it is a belief, and so i endeavour to live as though this is all we have, and that means living with an awareness of how precious each moment is, especially those spent with those we love, which takes us back to living in the moment, and not wasting our life living in our thoughts, ruminating about things that may or may not come to pass.
To go back to Buddhism, Buddha had very little to say about life after death or metaphysics in general. He accepted that we cannot know and so speculation was pointless and the only meaningful thing we could do was to seek to understand the nature of this life.