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(1) First ionisation enthalpy order $N>O>P>S$ is correct since N has a half-filled p-orbital making it stable with higher ionisation energy.
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(2) Negative electron gain enthalpy does not follow this order because O has more negative electron affinity than N. So $N>O$ is incorrect for electron gain enthalpy. Hence this statement is wrong.
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(3) Order $F>Cl>O>S$ for negative electron gain enthalpy is valid as halogens have high electron affinity.
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(4) Ionic size decreases with increasing positive charge, so $Fe^{3+}<Fe^{2+}<Fe$ is correct.