
Believe it or not, if our mums had to have antibiotics, I'd give each puppy a tiny amount of natural yogurt, on their tongues - probiotic, to counter any effect the antibiotics being given to mum and so perhaps coming through the milk might have on the puppies.
If she did take any of the placenta, that would account, I think for the farting. But as always with pregnancy, whelping and nursing, her system is bound to be a bit off. I too would have expected the vet to give a shot to clear out any retained birthing material, at the time. But if she's okay now, then she's okay! You'd be thinking about worming the puppies, and her, at 2 weeks bit I'm not sure I'd rush into that if their stools are not right. It does need to be done however.