That's sad, threelittlebabies.....it's good she is expressing (and I don't agree that the pump might be worse than the baby at getting the milk out - an ineffectively, sleepy, jaundiced baby may not be good at all) but she really has to do it often enough to build up a supply. She needs to express at least 8 times a day inc at night, otherwise it just won't happen.....:( Expressing when she gets round to it isn't enough.
I would be very worried about the baby not pooing and the fact the baby looks thin. From what you say, this baby does need formula at this stage, because for whatever reason, breastfeeding just isn't working.
Now, why is it not working? The pph will certainly have slowed things down, so a mother with a pph may well find her milk comes in later. Delayed milk production is a known effect of pph and your frind's was certainly serious. There is a rare condition called Sheehan's syndrome which is actually caused by pph - it affects the pituitary gland (which drives milk supply) and low milk production is the result. This is, I stress, very rare, and I have only ever read about it, and not come across anyone who had it.
I am not a medic, and I don't know if it is correct that it's the loss of hormones that causes the milk problem (and the replacement blood not having the hormones exacerbating it) but actually, it sounds plausible. That would only cause delay in the milk coming in, not wipe it out, though, and the literature suggests that if your friend continues to express often, and to put the baby to the breast, things will start to happen after 1-2 weeks.
This mother and her baby are not well. It sounds from what you say that she is doing her very best and that she has got some good medical and midwifery support - breastfeeding is obviously under threat here, but it can be saved. Immediate concern is ensuring the baby is fed, however this happens.
Hope she feels better soon.