Why must geostationary orbit at the equatorial plane?
Any object which is geostationary doesn't move relative to the surface.
If it isn't in the equatorial plane, it will oscillate between being in the northern and southern hemispheres.
It could be geosynchronous and be in another inclination, but not geostationary.
Because a geostationary orbit, like any orbit, revolves around the center of gravity. If an object is above the earth at the proper altitude for geostationary orbit, but it is North of the Equator (let's say 10 degrees, for this example), you can draw a line from the object through the surface of the earth to the earth's center. If you extend this line so it reaches the surface of the earth once again, on the far side, it will exit the earth at 10 degrees of southern latitude. The object in orbit must pass directly over this point at some time.
Separate names with a comma.