1. Northern Hemisphere winter is when the Earth is closest to the Sun. I'm not sure whether there are albedo effects that might mitigate that, but I'd thought that 3.3 % difference in proximity would mostly outweigh it. Perhaps there's a bit of a shift of the precise maximum towards late autumn, though, before the northern ice has built up?
2. Yes.
3. On Earth, or in Earth? The balance is between water added from space, water lost by photodissociation in the atmosphere, and water cycling into and out of the mantle via tectonics and volcanism. How that balance actually works out... well, I'm really not sure, but I'd guess the photodissociation and loss of hydrogen wins out. I once did some calculations on the expected initial water content of the Earth, based on a carbonaceous chrondite standard, and found that we've lost about 90% of what was originally there. Probably most of that went very early on, of course, but still.
As for the balance between the hydrosphere/atmosphere and the mantle, that's left as an exercise for the student.
Do I win a cookie?