Statement I:
Ionization enthalpy generally increases across a period from left to right.
However, Nitrogen (2s22p3) has a stable half-filled electronic configuration, making it harder to remove an electron compared to Oxygen (2s22p4).
Thus, the order is C<O<N<F.
Statement I is true.
Statement II:
For Group 16 elements, Oxygen has an exceptionally low magnitude of electron gain enthalpy due to its small size and high inter-electronic repulsions in the 2p subshell.
The magnitude of electron gain enthalpy decreases down the group from Sulphur onwards.
The correct order of magnitude is S>Se>Te>Po>O.
Statement II is true.
Both statements are correct.