I had a restless baby with colic who was up and down at night and I was my thinnest ever at that time. I guess sleep deprivation just made me haggard. You didn't say if you were breast feeding or not. I was, and I think that's one reason I went down to 103 pounds.
I was reading some sleep science last week that said it's very natural for many people to be awake at night for an hour or two, so I just wouldn't worry about it anymore if I was you.
I'm not up on the latest child care advice, but I would think it might be better for all three of you to begin getting the baby used to sleeping on his own. That way, if he awakens at four he might just fuss quietly a little bit and go back to sleep, rather than wake you up. A more solid routine would probably help you with your diet plan, too.
Your plan sounds mighty ambitious for a busy young mother. Might you just try giving up sugar? It's winter! I want you to have your coffee!
PS I had my baby in 1968 so take my advice with a big grain of salt. Haha. changed a little