My doctor said as long as its refrigerated after a feeding if there is still some left you can use it for the next feeding.
Warm it in hot water. I know my milk separates so warming it to breast temp is how I give it to my son (plus it makes the hubby feel included and I know I love the rotating night feedings to get a little extra sleep).
Ask your pedi they might have some advice as well! Congratulations!
If baby eats from the bottle I would only leave it for up to one hour and then discard, yes I would say that goes for breast milk too. Split into two bottles that way you won't waste more milk. It's great that baby is latching onto both you and bottle well but nipple confusion isn't always instant. I gave my daughter bottles of pumped milk on and off up until she was two weeks old and that was when she quit taking the breast and only wanted bottles. I had to use a nipple shield to get her back to breast. This doesn't always happen, just warning you!