Oh dear, Jens, we really do need to try to help you through this (and it's OK, I know saying "just snap out of it" doesn't work).
an unfailing tendency to give up on everything I try my hand at. As you probably understand, this often leads to internal conflict.
You're judging yourself by the standards you have learnt for the experienced world. You don't need to - when you do things you are learning to express yourself, which is not the same. Allow yourself to acknowledge some value in what you do, however half-baked you also think it is, and you will start to notice that others do as well (some, at least - let's be realistic here!). More confidence will come in due course.
but I don't want to be a teacher! My mother is, and she hates everything about it to bits.
I know happy teachers, too! And unhappy ones, I admit - but that's to do with the way the UK government controls schools at present, rather than teaching itself. In any case, it's not about what your mother likes, but just you. And you're way too young to know what you will do in the end, anyway.
Optional illustration:
I had decided my career (medicine) at the age of 12 (with some unconscious parental pressure), and got as far as applying to university based on that. I then realised this was not going to be me, and changed the course I was applying for (physics). During my time at university, I changed my course again (engineering science) and decided on three careers in turn, all as a result of acquaintances struck at university: building pipe organs - blown away by archaic apprenticeship rules (which were ended only a couple of years later); computing - I decided it would be a good hobby but a boring career; sound recording/reproduction... which made it - I joined the BBC at the end of my degree. Two years later I was doing a computing job in a medical context, and with some variations along the way I still am; my hobbies are music, sound recording/reproduction (in which I have a little very specialised international notoriety), and a particular interest in pipe organs. I have published an edition of a previously unpublished piece of music by Haydn, and a number of CDs - so in the end my hobbies have done more to define me publicly than my employment, even though I have always chosen a job I would enjoy in preference to one I wouldn't.So don't panic yet; try not to worry, even.
I don't know who I want to be, and I don't know who I am.
You don't really get to choose who you are, and it takes a lifetime to understand the deal you got. At least there will always be something to think about!
More seriously, develop your interests - these help define you (you do have interests, even if you're frustrated by how you're handling them - see above). Allow relationships to develop naturally, but don't sweat it; I didn't have a romantic relationship until I was 22, and I seem to have got through life OK without too much sense that I really missed out on anything.
I am mortally afraid of so many things. Global warming, mutating flu viruses, nuclear and biological warfare, [...] because anything that's going to help me in twenty years is useless - something is bound to have killed me by then anyway.
This time I
will try to say "snap out of it". I can't stop you worrying, but please don't succumb to the modern tendency to ignore the meaning of statistics. Things that are very unlikely to happen
are very unlikely to happen. Spend your efforts worrying about things which
are likely to happen; or, better, put the energy into doing something about them, or even generically improving your ability to deal with things in life, rather than worrying.
I may be over-sensitive on this one because I failed to get my own step-son (at exactly your age) out of a long period of nihilism brought on by a conviction that there would be global nuclear war before he reached 25. He wrecked his life at a crucial time, including a couple of years living rough - and although he is way out of it now, he did a lot of damage to his future during that period (and now sees it that way himself). Please don't go there - I don't know how to say more.
Paul