The field is created by the fixed charge at any point, whether or not there is a test charge.
A force will exist only if you place a charge on this pre-existing electric field. Remember a charge never experiences its own electrical field.
The field is orthogonal to the equipotentials at any point and always points in the direction of decreasing potential. The spherical symmetry of this charge distribution is revealed by its spherical equipotentials.
Click on the static charge in the center to change its sign.
Click on the charge to catch it. Throw it to set new initial conditions.