As mentioned before an em measurement is based on the parents font-size. If the parent is assumed to be 16px by default (although there are no guarantees that this is true for many reasons) then 10px would be 62.5% or .625em.
However you cannot assume that the default is 16px as the user may have changed the default or be using their own stylesheet.
2) Is it better to use em rather than px?
For scalable layouts and to preserve the ratio of changes between the elements on the page then ems are preferred. If you reduce a parents em font-size then the relationship between the parent and the children is automatically catered for (unlike using pixels which would mean only the parent would have changed size).
It can be tricky though and as ems are rounded up and down you will find the odd pixel difference here and there.
3) Why does my page not resize correctly when zooming in/out?
Because you have sized the elements in pixels and therefore when text is zoomed the elements can only expand vertically and not horizontally due to the width restrictions and the layout does not retain its correct aspect.
Most modern browsers these days however will allow you to zoom the whole page ok.