(A) Second IE of C vs B. Removing the second electron from boron means pulling it from the stable 2s${}^2$ configuration of B${}^{+}$ (1s${}^2$ 2s${}^2$), which requires extra energy. Removing the second electron from C${}^{+}$ (1s${}^2$ 2s${}^2$ 2p${}^1$) takes it from a 2p orbital, which is easier. So IE${}_2$(C) $<$ IE${}_2$(B). Correct.

(B) Isoelectronic ionic radii. Al${}^{3+}$, Mg${}^{2+}$, Na${}^{+}$ all have the Ne configuration. As nuclear charge increases (Z = 11, 12, 13) the radius decreases, so Al${}^{3+}$ $<$ Mg${}^{2+}$ $<$ Na${}^{+}$. Correct.

(C) Density of K vs Na. Although K has higher atomic mass, the increase in atomic volume from Na to K outpaces the mass increase, so density of K (0.86 g/cm${}^3$) is actually less than density of Na (0.97 g/cm${}^3$). Incorrect.

(D) H-H vs F-F bond strength. Bond dissociation energy of H-H is roughly 436 kJ/mol while F-F is only about 159 kJ/mol (weakened by lone-pair repulsion between the small F atoms). So H-H is stronger, not weaker. Incorrect.

$\therefore$ Correct options are (A) and (B).