The general trend for ionization energy across a period is to increase, but small decreases are observed between Be and B and again between N and O, making statement I incorrect.
These small decreases are due to the increased stability of the full and half full sublevels.
The 2s orbital in BeBe is full, making it more difficult to remove an electron from BeBe than BB, so BB has a lower ionization energy.
The 2p sublevel of NN is half full, making it more difficult to remove an electron from N than O.
The observed decrease is due to the half full sublevel of N, not the effective nuclear charge of O (O does have a greater effective nuclear charge, but this alone would cause an increase the ionization energy).