Where's the Prime Meridian of celestial coordinates
The equatorial plane and the ecliptic plane cross each other, like shown in this illustration:



The "Vernal Equinox" is simply the direction of the line where they cross.

You can not obtain the Earth latitude from the ecliptic latitude alone, as the planes are not parallel. You must know the ecliptic longitude as well.

From equatorial to Earth latitude it is much simpler, the latitude is equal to the declination.