Yes. If your baby is nursing every 2-3 hours during the first few days after birth, they will get all the colostrum they need. Average is about 5 ml per feed on day one, 10 ml per feed on day 2 and 15 ml per feed on day 3 (about 1/2 oz).......This is just enough to keep up the baby's blood sugar and provides a lot of antibodies.
Yes. Yes - babies are built to need very little to drink for the first few days. If your baby is feeding well with good latch, peeing a decent amount and has a stable weight pattern for the first few days, then whatever you are doing with the feeding is truly sufficient. No needs to worry about supplementing unless there is excessive weight loss or very bad jaundice.