Does the shapes of orbitals change with factors such as electric fields, magnetic fields,
In quantum mechanics, any new extra potentials , as an introduction of an electric or a magnetic field, will lead to new solutions for the orbitals.
Example : the Zeeman effect in hydrogen:
When an external magnetic field is applied, sharp spectral lines like the n=3→ 2 transition of hydrogen split into multiple closely spaced line
So one energy level splits into two because of the spin of the electron, and thus one orbital becomes two.
So it will depend on the specific problem.
No, temperature has to do with the average kinetic energy and possible interactions, it is not a field/potential
intense gravitational fields even with excitation of atom?
Again, a solution of the extra potential to the atomic potential has to be studied. Gravitational fields are weak, and also at the moment there is not unification of the three forces and gravity and only effective quantum mechanics exists for gravitational fields, so it will all be a matter of assumptions.
Will the electron just change its orbital and the shapes of orbitals would be unaffected?
For an electron to change an orbital, the atom has to absorb a photon of the appropriate energy. New solutions as in the Zeeman effect, can be considered as a change in orbital , but it is a different state, "atom + extra field".