familygirl - you are right, there is a ton of myth and misleading info out there. There is good research, though, so healthcare professionals have no good excuse for not sharing solid evidence.
Eating and drinking - there is virtually no evidence that what you eat and drink has any direct effect on breastfeeding (the oats thing harpsi mentions is something that is really no more than anecdotal, but I think it does seem to work for some mothers).
Low supply - the major reason for low supply is that the milk is ot being removed frequently or effectively enough. Resting makes little difference (except when it means the baby is fed more often, because the mother is taking her rest while feeding the baby).
There's no reason why tiredness should affect supply or 'performance' but individuals may have individual experiences of this.
Some babies do seem to find it more difficult - birth experiences may have an impact, which is why getting mothers and babies together and keeping them that way immediately post-birth is good.
Breast size really does not make any difference.
As harpsi says, kellymom.com is about the best resource for evidence and clear explanation.