Across a period (left to right), atomic radius decreases because nuclear charge increases while electrons are added to the same shell, so the increased effective nuclear charge pulls the electron cloud closer. Down a group, atomic radius increases because a new shell is added at each step and the number of inner shielding electrons increases, outweighing the rise in nuclear charge.

Nitrogen has the configuration 1s2 2s2 2p3 with a half-filled 2p subshell, which is extra stable due to symmetry and exchange energy, so removing an electron requires more energy. Oxygen (1s2 2s2 2p4) has one paired electron in 2p; removing it relieves electron-electron repulsion and gives a stable half-filled configuration, so less energy is needed. Hence IE1 of nitrogen > oxygen.

Ionization enthalpy is the minimum energy required to remove the most loosely bound electron from an isolated gaseous atom in its ground state. Across a period it increases because nuclear charge increases and atomic size decreases, so the electron is held more tightly. Down a group it decreases because atomic size increases and shielding by inner electrons increases, so the outer electron is more easily removed.

M(g) -> M+(g) + e-