Nope, most schools are not open year round. That's why child care is such a booming and lucrative industry. Many rely on other family members (especially retired) to look after kids, sometimes friends but usually family. Religious communities also setup ad hoc day care systems to my knowledge. If you don't find free or cheap care you pay the piper.
I guess that's compensated via salary (they earn around 2x-3x more than their European counterparts).
Well, it might be true for some positions, like engineering, but it definitively does not apply to all of them.