^^You can back step and also side step. Try flicking the stick backwards like a double tap. Also double tap up and down to sidestep.
For the bob & weave you have to do a quarter circle forward. Round 4 teaches you how to do this in the training. I'm sure on the retail version of Champion there will training as well. I remember it was hard at first in round 4, so you just got to practice it. I became a master at it but it doesn't seem as effective on champion or I don't have the timing down yet.
Punch modifier adds more power to your shots. So if you want a really strong and stiff jab add the modifier. You want a devastating hook add the modifier. The downside to it is it takes more stamina and if you get countered or miss you can pay consequences.
Check this out for more tips:
http://www.ea.com/fight-night/blog/controls-tutorial