Step 1: Check statement I.
The first ionization enthalpy decreases down a group and generally increases across a period.
The correct order is
\[
\boxed{\mathrm{Li}>\mathrm{Be}>\mathrm{B}>\mathrm{Mg}.}
\]
Hence, statement I is correct.
Step 2: Check statement II.
The correct order among the given elements is
\[
\boxed{\mathrm{P}>\mathrm{Mg}>\mathrm{Al}>\mathrm{Na}.}
\]
Hence, statement II is correct.
Step 3: Check statement III.
Because of the extra stability of half-filled \(2p^3\) configuration,
\[
\mathrm{N}>\mathrm{O}.
\]
Also,
\[
\mathrm{F}>\mathrm{N}>\mathrm{O}>\mathrm{C}.
\]
Thus, statement III is incorrect.
Therefore, only statements I and II are correct.
Hence,
\[
\boxed{\text{Correct answer: I and II only}.}
\]
Therefore, the correct option is \(\boxed{(D)}\).