Wow you look sooooooooo much better ... did you decide to take lessons or how did you go about doing it? I have to give you kudos for taking initiative to correct things- so many people won't do that and it makes me mad! Lol
So for your back- think about sucking in your tummy and sitting up tall. If you suck in your tummy you can't arch your back like that :) Also try and roll you hips under you a little bit rather then sticking your butt out.
Remember to keep those eyes up
When jumping I would like to see you shorten your sturrups and sink down deeper into your heels- also try to keep those toes a little more forward.
Keep up the good work!
**sorry if I repeated what others said... I didn't read the others comments