Baby oil on baby's bum helps at diaper changes so the meconium doesn't stick. Then you aren't scrubbing baby's bum so hard to get it off next change.
Both breast let down even though you are only using one (I didn't know this the first time). I keep a burp cloth to soak up the milk from the unused breast.
My let down is a prickly feeling but I also feel nauseous for a moment during let down. My midwife says this is normal for some women. Oh, and yes, let down after orgasm has gotten my husband's chest wet LOTS of times

Baby girls can have a few drops of blood from the vagina in their diapers as a result of mama's hormones still circulating in their bloodstream right after birth. Boys scrotum will be swollen for the same reason. Both sexes may have drops of "witches milk" from the breasts.
Vernix is like baby cold cream. Just rub it in to baby's skin. Don't let anybody try to wash it off, it's not dirty. It is in all of the little creases and will re-absorbe without nurses trying to painfully scrub it out.
Some babies want to nurse every hour. Breastmilk is digested so easily and a one day old baby's tummy is the size of a marble. But, babies want to nurse for lots of reasons other than hunger too. It can be frustrating but baby just loves mama and wants to be close, or is cold, or scared, or frustrated, or lonely, etc.