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From Mössbauer and resistivity measurements on 57Fe-doped La2-xSrxCuO4, we have explored the phase diagram of the series for 0≤x ≤0.30 and $1.5~{\rm K} \leq T \leq 295$ K and we have studied the local magnetic properties in the semiconducting, superconducting, and normal metallic phases. The most outstanding result concerns the coexistence over part ($0.06 \lesssim x \lesssim 0.16$) of the total ($0.06 \lesssim x \lesssim 0.25$) superconducting range of two different fractions showing different local behaviours. The first fraction corresponds to intrinsic spin-freezing, below ∼8 K, in the Cu sublattice. The relative sample volume of this fraction which is attributed to semiconducting domains decreases as x increases. In the second fraction which is presumably superconducting, there is no evidence of intrinsic Cu moments, however iron induced local magnetic order is present. In the semiconducting fraction the Cu magnetic moments remain essentially parallel to the basal plane, while in the superconducting fraction the iron-induced local magnetization moves towards the c axis as x increases. We have performed accurate 57Fe hyperfine measurements in an argon annealed quasi-stoichiometric La2CuO4 sample and we have observed an abrupt variation of the magnetization near the Néel temperature. In an air annealed La2CuO4+y sample, we have evidenced the presence of oxygen interstitials and we have shown that the effective interlayer magnetic coupling is strongly reduced with respect to the y=0 sample

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