I be a trumpet player, but as for number two on your list...
For jazz anyway, get to know your scales, blues and otherwise (though scales are good in concert band too). Also get an Abersold CD - that's basically just a rhythm section with chord progressions and such - and play. Screw around and get used to improving, just making stuff up, trying to develop melodic ideas instead of just playing notes strung together.
Although...it would help if you learned how to play sax first, since I get the impression you've never played it before....can't help you there! Take private lessons, if you can afford it...I took them from 6th through 8th grade and they helped me so much, I wish my teacher was still around because he was incredible.
Good luck switching from brass to woodwind - I hope I never have to, I love my trumpet too much