A changing electric field produces a magnetic field, but if the electric field is spherical, this would mean that the field strength around the electric charge would be independent of such rotation, so my question is: does a spinning spherically symmetrical electric charge create a magnetic field?
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2$\begingroup$ Magnetic field aren't only caused by changing electric fields, a spinning non-pointlike charged object constitutes a current. $\endgroup$– TriatticusFeb 27 at 5:17
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Yes. Any spinning charged object has a magnetic moment that produces a magnetic field. The magnetic moment of a spinning object is given in terms its angular momentum as ${\vec\mu}=G{\vec L}$, where $G$ is called the gyromagnetic ratio. This is described in any electromagnetism textbook