Can't remember about the breastmilk. I think it was really long, like 12 hours or something. Then again, maybe I'm crazy!
As for crying to sleep, definitely not at that age, IMO. I wrap baby up, arms snuggled in tightly, lay him/her down after nursing and almost asleep, and I have pretty good luck at baby falling asleep. If you use a pacifier, it comes in handy at this time too. It gets much more challenging the more mobile they get!
Often I stay in the room, folding laundry or something - or am in/out quickly doing things - the baby will watch and doze off. If the baby literally only fusses a few times, I'll leave him, or if it's few and far between, I'll leave him. But if he's actually really crying and it's obvious it's not going to stop really quickly, I pick him up or pat or something.
After my first, I decided I didn't want baby nursing to sleep. It got too demanding (especially once I had others I needed to take care of too). so, I totally hear you on your desire for that! When they are newborns, I let them nurse to sleep. As they get older, it's easier to not (at least with mine).
But, I'm not a cry-it-out type of person. I will holding/rock a crying baby, but I don't consider that crying it out at all. My baby is 12 months old now. And, if she wakes up at night and cries, I'll wait before going in and see if she settles back to sleep. But it's only a few minutes at the most. Usually she settles right back to sleep! I finally discovered that once. Usually I would run right in and grab her and feed her and get her back to sleep - often taking an hour before she was asleep enough to stay asleep when I laid her down (usually I co-sleep, but she won't sleep! my first child out of four that seems to prefer her own space...so odd..but I do sleep much more solidly now). Anyway, but one time I couldn't get to her right away, and she went back to sleep on her own. So, now I wait a few to see if she'll settle back down. I don't consider that crying it out either.
I'm rambling, as usual.
Hope that helps some. In my opinion, your baby is way too little to cry it out. If he fusses or something, I get leaving him and waiting to see if it turns into real crying or if he falls asleep before doing anything. Making sure he's wrapped up nice and snug helps tremendously too. Good luck!
Oh, and babysleepsite.com (or google "the baby sleep site") has great info for what to expect with how much they should/shouldn't sleep. Each child is different, but as they age, it can get confusing not being sure how much sleep they need because it changes so often. I'm not a scheduler, but I'm definitely a person who loves routine! It's a very helpful site.