In the Newtonian framework no, a freely falling frame is not inertial because it is accelerating with respect to some fixed background inertial frame. In the GR framework, a freely falling frame is locally inertial.
In Newtonian mechanics it is not an inertial frame (however you can still do Newtonian mechanics in this frame as long as you transform to the frame correctly). In GR, it is locally an inertial frame and locally you can do SR.
ok here is a question I have had for a while related to that. Lets say there is a charged spherical shell around me and the earth, and I am orbiting the earth, and the charged spherical shell is rotating with me at a constant
[itex] \omega [/itex] so relative to me the charged spherical shell is not moving and the shell is just slightly at a larger radius than me. But to someone standing on earth the shell is rotating, and in their frame this will produce a B field that points up and is constant. whats going on.
Actually even when you are in the frame of an observer rotating exactly with the (slowly) rotating shell of charge, there will be a non-zero magnetic field observed in the rotating frame due to fictitious currents. You have to be careful about how ##E## and ##B## fields transform from inertial frames to rotating frames, which are non-inertial. It is not as simple as transforming the fields from one inertial frame to another. For a detailed calculation of the scenario you described, see here: http://www.hep.princeton.edu/~mcdonald/examples/rotatingshell.pdf