you can certainly be born with a favourable genetic make-up to be good at sport (tall and want to be a basketball player for example) but no athlete can become good at their sport without meticulous practice and training. Psychologists believe that the most amount of meaningful practice you can squeeze into a year is around 1000 hours, and it takes 10 years working at this level to reach world class. This rule appears to apply to all endeavours, including getting good at a musical instrument. It also forms the basis for why we spend so much time at school.
good answer already from Jemma on this one but you will hear varying views.
Training is necessary but for all of the will in the world, you still need natural ability. In some respects, I would say you are more born an athlete than become one through training but you will not make it to the top without training.