Can someone please explain to me how to visualize an electromagnetic wave in 3D space?
The wikipedia article on electromagnetic radiation is clear enough.
The electromagnetic waves that compose electromagnetic radiation can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This diagram shows a plane linearly polarized EMR wave propagating from left to right (X axis). The electric field is in a vertical plane (Z axis) and the magnetic field in a horizontal plane (Y axis). The electric and magnetic fields in EMR waves are always in phase and at 90 degrees to each other.
This is one optical ray from the source,and the colored part is how the functions describing the strength of the electric and magnetic field change in space with a wave pattern.
Does the wave amplitude represent how high the wave goes (to the ceiling)?
No, what are waving are the strengths of the E and B fields.
And howcome it looks like a sphere? Why is it shaped like that,
A source of electromagnetic waves, like an antenna impose a pattern that releases in spherical optical rays the wave depicted above , because of the geometry and the nature of wave solutions to the elecromagnetic equations. As the other answer says, it is a three dimensional radiation and will be distributed radially , similar to a two dimensional source of a disturbance of the surface of a lake which is distributed circularly.
does the electric field vector play a role in this shape?
Yes, it is the electric and magnetic fields that vary in space as the wave propagates.
This 3D animation shows a plane linearly polarized wave propagating from left to right. Note that the electric and magnetic fields in such a wave are in-phase with each other, reaching minima and maxima together