What are the products formed when lanthanoids $(Ln)$ react with $1$. $H_2O$ and $2$. $N_2$?

Which of the following elements are included in the lanthanoid series?

Fill in the blanks:
$1.$ In the elements of the actinoid series,the last electron enters the ........... orbitals.
$2.$ Inner transition elements are the elements of the .......... series.
$3.$ If electrons are filled in the $5f$ series,those elements are called ....... elements.
$4.$ Many elements of the actinoid series are ......... .

Among $Ce(4f^{1} 5d^{1} 6s^{2})$,$Nd(4f^{3} 6s^{2})$,$Eu(4f^{7} 6s^{2})$ and $Dy(4f^{10} 6s^{2})$,the elements having highest and lowest $3^{rd}$ ionisation energies,respectively are

What is the number of unpaired electrons present in $f$-orbital at $+3$ oxidation state of $Lu (Z=71)$?

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