Which element in the lanthanoids is radioactive?

Which of the following statements are correct?
$I$. $P$ has the least negative electron gain enthalpy among $P, S, Cl$, and $F$.
$II$. In $Eu$ and $Yb$, lanthanoid contraction is not observed.
$III$. $Ce(OH)_3$ is the most basic among lanthanoid hydroxides.
$IV$. The radii of $Na$ and $Na^+$ are $95 \ pm$ and $186 \ pm$ respectively.

Arrange the ions $Ce^{3+}$,$La^{3+}$,$Pm^{3+}$,and $Yb^{3+}$ in the increasing order of their ionic radii.

Although $(+3)$ oxidation state is the characteristic oxidation state of lanthanoids,cerium shows $(+4)$ oxidation state also. Why?

$4f^2$ electronic configuration is found in

Identify the ion having $4f^6$ electronic configuration.