My eczema is actually worse in the summer, I think it's because i'm more active and I garden, so I am showering and washing my hands a lot more often (mine is almost exclusively on the palm of my left hand and my thumbs). Or should I say, the peeling skin is worse in the summer, I don't actually get more bumps in more places.
From years of dealing with it, I can tell you that the best thing anyone can do is destress, keep your skin moisturized with a good lotion, not some stinky crap from the mall (I like Nature's Gate), try not to overwash, switch out your soaps/laundry detergents for something gentle, and the hydrocoristone cream should help with the itching. I've never been officially treated for mine, but I believe if you go to the doctor they will give you a steroid cream.
I don't know about the night sweats, but excessive sweating is also thought to be a possible cause of eczema outbreaks. The kind that I have is usually linked to excessive sweating (but I actually don't sweat very much, so who knows):http://en.wikipedia.org/wiki/Dyshidrosis
I found out that dairy was a big trigger for me, after I switched to soy milk and yogurt it got a LOT better. I've gone gluten-free and low sugar for periods of time and those don't seem to be an issue for me, but everyone is different.