new mom feeding advice please! baby won't eat

I had my baby on the 13th at 35 weeks and it's so hard to feed him, he latched very well and I make a good amount of colostrum/milk but I have a hard time attaching him to my nipple and getting him to stay awake to eat. He'll suck two times really good and just fall asleep and then suck once and pass back out. The nurses and lactation consultant said it's normal and to his wake him up but I'm having a hard time now that I'm home and really need advice on what to do. I've been supplementing with today  formula to make sure he's eating enough because he seems like he isn't getting much from nursing and he likes bottles way more. 😓 what should I do? I really want to breast feed him. He's also only 5 pounds and idk how much to feed him..
I tried pumping but I don't know how long the milk is good for? If I put it in the fridge or freezer how long does it last? If I leave it out how long is it okay?