My tummy had noticeably gone down the next day and as LadyBeeley said breastfeeding even just in that first week helps your uterus contract and go down. My dr never told me to massage it, maybe because I had a csection, but he and the nurses regularly measured my tummy to see if my uterus was shrinking. I also had a physio come round and check how big the tummy muscle separation was give me some exercises to help.
Yes breastfeeding does. Within 24hrs ur uterus is half the size it was before and I believe each week after that it doubles down. After birth the dr will tell you where to rub on your tummy to massage your uterus. You really need to do that to recover quickly and healthily. I breastfed and lost the 36lbs I gained by 9 days PP. Hope this helps.