I play just about all of them to some degree. Started on flute, and switched to french horn which was my major instrument all through college. I never played jazz on sax, so I can't help you much there...aside from the general advice of learning your scales and arpeggios, as well as the regular chord progressions found in jazz music...to better help you with improvization. With high notes on trumpet, in the long term it's all about air flow and embouchure control/endurance. The embouchure, like any muscle, just takes time to build...and will get better the more you play higher parts. In the short term, more pressure of the mouthpiece against the lips can help...but isn't a good longterm solution for regular playing...as it tires the lips much much sooner, and if you do it too much can bruise the muscles a little. (happened to me once or twice. Generally heals in a couple of days, just feels very sore when you play).
