The structure, elemental abundances, physical conditions of the LMC supernova remnant (SNR) 0540-69.3 and its surroundings were investigated using [O III] imaging and spectroscopy. Several new spectral lines are identified, both in central filaments and in interstellar clouds shocked by the supernova blast wave. The central lines are redshifted by $440pm80$ km s$^{-1}$ with respect to the LMC, and the [O III] emission displays a symmetry axis of ring-like structures which could indicate that the pulsar shares the same general redshift as the central supernova ejecta. [O II], [S II], [Ar III] and H$beta$ have more compact structures than [O III], and possibly [Ne III]. The average [O III] temperature is $23,500 pm 1,800$ K, and the electron density from [S II] is typically $10^3$ cm$^{-3}$. By mass, the relative elemental abundances of the central shocked ejecta are ${rm O:Ne:S:Ar} approx 1:0.07:0.10:0.02$, consistent with explosion models of $13-20$ solar mass progenitors, and similar to that of SN 1987A, as is also the mixing of hydrogen and helium into the center. [O III] is also seen in freely coasting ejecta outside the pulsar-wind nebula out to well above $2,000$ km s$^{-1}$. From this a pulsar age of $approx 1,200$ years is estimated. Four filaments of shocked interstellar medium with a wide range in degree of ionization of iron are identified. One was observed in X-rays, and another has a redshift of $85pm30$ km~s$^{-1}$ relative to LMC. From this the electron density of the [O III]-emitting gas is estimated to be $10^3$ cm$^{-3}$. The line of the most highly ionized ion, [Fe XIV] $lambda$5303, likely comes from an evaporation zone in connection with the radiatively cooled gas emitting, e.g., [O III].
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