Yes. It is inertial to first order in spacetime derivatives on the free-falling worldline, so local means, in part, at a point. Even at this point, it is not inertial at second order. The technical implementation of this is called "Fermi normal coordinates". The restriction to first order at a point is the technical implementation of "local" in the statement of the equivalence principle.
Yes. For points near a free-falling wordline, Fermi normal coordinates shows in an order by order expansion how they deviate from inertiality. For points near the free-falling worldline, the deviations may be so small as to be negligible. In practice, "near the worldline" is large enough to include entire particle accelerators, which only take SR into account, not GR (unless they use GPS, like OPERA